RD Sharma Class 11 Solutions Chapter - Probability | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


33. Probability
Exercise 33.1
1. Question
A coin is tossed once. Write its sample space.
Answer
Given: A coin is tossed once.
To Find: Write its sample space?
Explanation: Here, the coin is tossed only once,
Then, there are two probability either Head(H) or Tail(T)
So, Sample will be
S = {H, T}
Where, H denotes Head and T denotes Tail
Hence, The sample is {H, T}
2. Question
If a coin is tossed two times, describe the sample space associated to this experiment.
Answer
Given: If Coin is tossed twice times.
To Find: Write the sample space associated to this experiment.
Explanation: Here, two coins are tossed, that means two probability will occur at same time
So, The sample space will be
S={HT, TH, HH, TT}
Hence, Sample space is {HT, HH, TT, TH}
3. Question
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this
experiment.
Answer
Given: If a coin is tossed three times .
To Find: Write the sample space for the given experiment.
Explanation: Here, the coins is tossed three time, then the no. of samples
2
3
=8
So, The sample space will be
S={HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
Hence, The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Question
Write the sample space for the experiment of tossing a coin four times.
Answer
Given: A coin is tossed four times.
Page 2


33. Probability
Exercise 33.1
1. Question
A coin is tossed once. Write its sample space.
Answer
Given: A coin is tossed once.
To Find: Write its sample space?
Explanation: Here, the coin is tossed only once,
Then, there are two probability either Head(H) or Tail(T)
So, Sample will be
S = {H, T}
Where, H denotes Head and T denotes Tail
Hence, The sample is {H, T}
2. Question
If a coin is tossed two times, describe the sample space associated to this experiment.
Answer
Given: If Coin is tossed twice times.
To Find: Write the sample space associated to this experiment.
Explanation: Here, two coins are tossed, that means two probability will occur at same time
So, The sample space will be
S={HT, TH, HH, TT}
Hence, Sample space is {HT, HH, TT, TH}
3. Question
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this
experiment.
Answer
Given: If a coin is tossed three times .
To Find: Write the sample space for the given experiment.
Explanation: Here, the coins is tossed three time, then the no. of samples
2
3
=8
So, The sample space will be
S={HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
Hence, The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Question
Write the sample space for the experiment of tossing a coin four times.
Answer
Given: A coin is tossed four times.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coins is tossed four time, then the no. of samples
2
4
=16
So, The sample space will be
S={HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT,
TTTH}
Hence, The sample space is {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH,
TTHH, HTTT, THTT, TTHT, TTTH}
5. Question
Two dice are thrown. Describe the sample space of this experiment.
Answer
Given: Two dice are thrown.
To Find: Write the sample space for the given experiment.
Explanation: We know there are 6 faces on a dice. Contains (1, 2, 3, 4, 5, 6).
But, Here two dice are thrown, then we have two faces of dice (one of each)
So, The total sample space will be 6
2
 = 36
Now, the sample space is:
S={(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1)(3, 2), (3, 3), (3,
4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), 5, 4), (5, 6), (5, 5), (6, 1), (6, 2),
(6, 3), (6, 4), (6, 5), (6, 6)}
6. Question
What is the total number of elementary events associated to the random experiment of throwing three dice
together?
Answer
Given: Three dice is rolled together.
To Find: What is the total number of elementary events.
Explanation: Here, three dice are thrown together,
And, There are 6 faces on die,
So, The total number of elementary event on throwing three dice are
6×6×6=216
Hence, The total number is 216
7. Question
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
Answer
Given: A coin is tossed and a die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coin is tossed and die is thrown.
We know, when coin is tossed there will be 2 events either Head or Tail.
And, when die is thrown then there will be 6 faces (1, 2, 3, 4, 5, 6)
Page 3


33. Probability
Exercise 33.1
1. Question
A coin is tossed once. Write its sample space.
Answer
Given: A coin is tossed once.
To Find: Write its sample space?
Explanation: Here, the coin is tossed only once,
Then, there are two probability either Head(H) or Tail(T)
So, Sample will be
S = {H, T}
Where, H denotes Head and T denotes Tail
Hence, The sample is {H, T}
2. Question
If a coin is tossed two times, describe the sample space associated to this experiment.
Answer
Given: If Coin is tossed twice times.
To Find: Write the sample space associated to this experiment.
Explanation: Here, two coins are tossed, that means two probability will occur at same time
So, The sample space will be
S={HT, TH, HH, TT}
Hence, Sample space is {HT, HH, TT, TH}
3. Question
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this
experiment.
Answer
Given: If a coin is tossed three times .
To Find: Write the sample space for the given experiment.
Explanation: Here, the coins is tossed three time, then the no. of samples
2
3
=8
So, The sample space will be
S={HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
Hence, The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Question
Write the sample space for the experiment of tossing a coin four times.
Answer
Given: A coin is tossed four times.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coins is tossed four time, then the no. of samples
2
4
=16
So, The sample space will be
S={HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT,
TTTH}
Hence, The sample space is {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH,
TTHH, HTTT, THTT, TTHT, TTTH}
5. Question
Two dice are thrown. Describe the sample space of this experiment.
Answer
Given: Two dice are thrown.
To Find: Write the sample space for the given experiment.
Explanation: We know there are 6 faces on a dice. Contains (1, 2, 3, 4, 5, 6).
But, Here two dice are thrown, then we have two faces of dice (one of each)
So, The total sample space will be 6
2
 = 36
Now, the sample space is:
S={(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1)(3, 2), (3, 3), (3,
4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), 5, 4), (5, 6), (5, 5), (6, 1), (6, 2),
(6, 3), (6, 4), (6, 5), (6, 6)}
6. Question
What is the total number of elementary events associated to the random experiment of throwing three dice
together?
Answer
Given: Three dice is rolled together.
To Find: What is the total number of elementary events.
Explanation: Here, three dice are thrown together,
And, There are 6 faces on die,
So, The total number of elementary event on throwing three dice are
6×6×6=216
Hence, The total number is 216
7. Question
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
Answer
Given: A coin is tossed and a die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coin is tossed and die is thrown.
We know, when coin is tossed there will be 2 events either Head or Tail.
And, when die is thrown then there will be 6 faces (1, 2, 3, 4, 5, 6)
SO, The total number of Sample space together is 2×6 = 12
S={(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
Hence, Sample space are {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
8. Question
A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space
for this experiment.
Answer
Given: A coin is tossed and the a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: Here, we have a coin and a die,
We know, when coin is tossed there will be 2 event Head and tail,
According to question, If Head occurs on coin then Die will rolled out otherwise not.
So, the sample spaces are :
S={(T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
Hence, Sample space is (T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)
9. Question
A coin is tossed twice. If the second throw results I a tail, a die is thrown. Describe the sample space for this
experiment.
Answer
Given: A coin is tossed twice. If the second throw results I a tail, A die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: When a coin tossed twice, Then sample spaces for only coin will be: {HH, TT, HT , TH}
Now, According to question , when we get Tail in second throw, then a dice is thrown.
So, The total number of elementary events are 2+(2×6)=14
And sample space will be
S={HH, TH, (HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2), (TT, 3), (TT, 4), (TT, 5), (TT, 6)}
Hence, this is the sample space for given experiment.
10. Question
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the
first toss, then a die is tossed once. Find the sample space.
Answer
Given: A coin is tossed and a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.
The possible outcome for coin is 2 = {H, T}
And, The possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}
If the outcome for the coin is tail then sample space is S1={(T, 1)(T, 2)(T, 3)(T, 4)(T, 5)(T, 6)}
If the outcome is head then the sample space is S2={(H, H)(H, T)}
So, The required outcome sample space is S=S1 S2
Page 4


33. Probability
Exercise 33.1
1. Question
A coin is tossed once. Write its sample space.
Answer
Given: A coin is tossed once.
To Find: Write its sample space?
Explanation: Here, the coin is tossed only once,
Then, there are two probability either Head(H) or Tail(T)
So, Sample will be
S = {H, T}
Where, H denotes Head and T denotes Tail
Hence, The sample is {H, T}
2. Question
If a coin is tossed two times, describe the sample space associated to this experiment.
Answer
Given: If Coin is tossed twice times.
To Find: Write the sample space associated to this experiment.
Explanation: Here, two coins are tossed, that means two probability will occur at same time
So, The sample space will be
S={HT, TH, HH, TT}
Hence, Sample space is {HT, HH, TT, TH}
3. Question
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this
experiment.
Answer
Given: If a coin is tossed three times .
To Find: Write the sample space for the given experiment.
Explanation: Here, the coins is tossed three time, then the no. of samples
2
3
=8
So, The sample space will be
S={HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
Hence, The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Question
Write the sample space for the experiment of tossing a coin four times.
Answer
Given: A coin is tossed four times.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coins is tossed four time, then the no. of samples
2
4
=16
So, The sample space will be
S={HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT,
TTTH}
Hence, The sample space is {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH,
TTHH, HTTT, THTT, TTHT, TTTH}
5. Question
Two dice are thrown. Describe the sample space of this experiment.
Answer
Given: Two dice are thrown.
To Find: Write the sample space for the given experiment.
Explanation: We know there are 6 faces on a dice. Contains (1, 2, 3, 4, 5, 6).
But, Here two dice are thrown, then we have two faces of dice (one of each)
So, The total sample space will be 6
2
 = 36
Now, the sample space is:
S={(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1)(3, 2), (3, 3), (3,
4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), 5, 4), (5, 6), (5, 5), (6, 1), (6, 2),
(6, 3), (6, 4), (6, 5), (6, 6)}
6. Question
What is the total number of elementary events associated to the random experiment of throwing three dice
together?
Answer
Given: Three dice is rolled together.
To Find: What is the total number of elementary events.
Explanation: Here, three dice are thrown together,
And, There are 6 faces on die,
So, The total number of elementary event on throwing three dice are
6×6×6=216
Hence, The total number is 216
7. Question
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
Answer
Given: A coin is tossed and a die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coin is tossed and die is thrown.
We know, when coin is tossed there will be 2 events either Head or Tail.
And, when die is thrown then there will be 6 faces (1, 2, 3, 4, 5, 6)
SO, The total number of Sample space together is 2×6 = 12
S={(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
Hence, Sample space are {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
8. Question
A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space
for this experiment.
Answer
Given: A coin is tossed and the a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: Here, we have a coin and a die,
We know, when coin is tossed there will be 2 event Head and tail,
According to question, If Head occurs on coin then Die will rolled out otherwise not.
So, the sample spaces are :
S={(T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
Hence, Sample space is (T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)
9. Question
A coin is tossed twice. If the second throw results I a tail, a die is thrown. Describe the sample space for this
experiment.
Answer
Given: A coin is tossed twice. If the second throw results I a tail, A die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: When a coin tossed twice, Then sample spaces for only coin will be: {HH, TT, HT , TH}
Now, According to question , when we get Tail in second throw, then a dice is thrown.
So, The total number of elementary events are 2+(2×6)=14
And sample space will be
S={HH, TH, (HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2), (TT, 3), (TT, 4), (TT, 5), (TT, 6)}
Hence, this is the sample space for given experiment.
10. Question
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the
first toss, then a die is tossed once. Find the sample space.
Answer
Given: A coin is tossed and a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.
The possible outcome for coin is 2 = {H, T}
And, The possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}
If the outcome for the coin is tail then sample space is S1={(T, 1)(T, 2)(T, 3)(T, 4)(T, 5)(T, 6)}
If the outcome is head then the sample space is S2={(H, H)(H, T)}
So, The required outcome sample space is S=S1 S2
S={(T, 1)(T, 2)(T, 3)(T, 4)(T, 5)(T, 6)(H, H)(H, T)}
Hence, The sample space for the given experiment.
11. Question
A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head,
we throw a die. Find the sample space of this experiment.
Answer
Given: A coin is tossed and there is box which contain 2 red and 3 black balls.
To Find: Write the sample space for the given experiment.
Explanation: when coin is tossed , there are 2 outcome {H, T}
According to question, If tail turned up, the a ball is drawn from a box.
So, Sample for This experiment S
1
 = {(T, R
1
)(T, R
2
)(T, B
1
)(T, B
2
)(T, B
3
)}
Now, If Head is turned up, then die is rolled
So, Sample space for this experiment S
2
={(H, 1)(H, 2)(H, 3)(H, 4)(H, 5)(H, 6)}
The required sample space will be S = S
1
  S
2
So, S={(T, R
1
), (T, R
2
), (T, B
1
), (T, B
2
), (T, B
3
), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
Hence, S is the elementary events associated with the given experiment.
12. Question
A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this
experiment.
Answer
Given: A coin is tossed repeatedly until comes up fro the first time.
To Find: Write the sample space for the given experiment.
Explanation: In the given Experiment, a coin is tossed and if the outcome is tail the experiment is over ,
And, if the outcome is Head then the coin is tossed again.
In the second toss also if the outcome is tail then experiment is over, otherwise coin is tossed again.
This process continues indefinitely
SO, The sample space for this experiment is
S={T, HT, HHT, HHHT, HHHHT…}
Hence, S is th sample space for the given experiment.
13. Question
A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement.
Write the sample space for this experiment.
Answer
Given: A box contains 1 red and 3 black balls.
To Find: Write the sample space for the given experiment.
Explanation: We have 1 red and 3 black balls in a box.
Let Assume Red = R
Let Assume Blue = B
Page 5


33. Probability
Exercise 33.1
1. Question
A coin is tossed once. Write its sample space.
Answer
Given: A coin is tossed once.
To Find: Write its sample space?
Explanation: Here, the coin is tossed only once,
Then, there are two probability either Head(H) or Tail(T)
So, Sample will be
S = {H, T}
Where, H denotes Head and T denotes Tail
Hence, The sample is {H, T}
2. Question
If a coin is tossed two times, describe the sample space associated to this experiment.
Answer
Given: If Coin is tossed twice times.
To Find: Write the sample space associated to this experiment.
Explanation: Here, two coins are tossed, that means two probability will occur at same time
So, The sample space will be
S={HT, TH, HH, TT}
Hence, Sample space is {HT, HH, TT, TH}
3. Question
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this
experiment.
Answer
Given: If a coin is tossed three times .
To Find: Write the sample space for the given experiment.
Explanation: Here, the coins is tossed three time, then the no. of samples
2
3
=8
So, The sample space will be
S={HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
Hence, The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Question
Write the sample space for the experiment of tossing a coin four times.
Answer
Given: A coin is tossed four times.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coins is tossed four time, then the no. of samples
2
4
=16
So, The sample space will be
S={HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT,
TTTH}
Hence, The sample space is {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH,
TTHH, HTTT, THTT, TTHT, TTTH}
5. Question
Two dice are thrown. Describe the sample space of this experiment.
Answer
Given: Two dice are thrown.
To Find: Write the sample space for the given experiment.
Explanation: We know there are 6 faces on a dice. Contains (1, 2, 3, 4, 5, 6).
But, Here two dice are thrown, then we have two faces of dice (one of each)
So, The total sample space will be 6
2
 = 36
Now, the sample space is:
S={(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1)(3, 2), (3, 3), (3,
4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), 5, 4), (5, 6), (5, 5), (6, 1), (6, 2),
(6, 3), (6, 4), (6, 5), (6, 6)}
6. Question
What is the total number of elementary events associated to the random experiment of throwing three dice
together?
Answer
Given: Three dice is rolled together.
To Find: What is the total number of elementary events.
Explanation: Here, three dice are thrown together,
And, There are 6 faces on die,
So, The total number of elementary event on throwing three dice are
6×6×6=216
Hence, The total number is 216
7. Question
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
Answer
Given: A coin is tossed and a die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: Here, The coin is tossed and die is thrown.
We know, when coin is tossed there will be 2 events either Head or Tail.
And, when die is thrown then there will be 6 faces (1, 2, 3, 4, 5, 6)
SO, The total number of Sample space together is 2×6 = 12
S={(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
Hence, Sample space are {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
8. Question
A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space
for this experiment.
Answer
Given: A coin is tossed and the a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: Here, we have a coin and a die,
We know, when coin is tossed there will be 2 event Head and tail,
According to question, If Head occurs on coin then Die will rolled out otherwise not.
So, the sample spaces are :
S={(T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
Hence, Sample space is (T, (H, 1)(H, 2), (H, 3), (H, 4), (H, 5), (H, 6)
9. Question
A coin is tossed twice. If the second throw results I a tail, a die is thrown. Describe the sample space for this
experiment.
Answer
Given: A coin is tossed twice. If the second throw results I a tail, A die is thrown.
To Find: Write the sample space for the given experiment.
Explanation: When a coin tossed twice, Then sample spaces for only coin will be: {HH, TT, HT , TH}
Now, According to question , when we get Tail in second throw, then a dice is thrown.
So, The total number of elementary events are 2+(2×6)=14
And sample space will be
S={HH, TH, (HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2), (TT, 3), (TT, 4), (TT, 5), (TT, 6)}
Hence, this is the sample space for given experiment.
10. Question
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the
first toss, then a die is tossed once. Find the sample space.
Answer
Given: A coin is tossed and a die is rolled.
To Find: Write the sample space for the given experiment.
Explanation: In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.
The possible outcome for coin is 2 = {H, T}
And, The possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}
If the outcome for the coin is tail then sample space is S1={(T, 1)(T, 2)(T, 3)(T, 4)(T, 5)(T, 6)}
If the outcome is head then the sample space is S2={(H, H)(H, T)}
So, The required outcome sample space is S=S1 S2
S={(T, 1)(T, 2)(T, 3)(T, 4)(T, 5)(T, 6)(H, H)(H, T)}
Hence, The sample space for the given experiment.
11. Question
A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head,
we throw a die. Find the sample space of this experiment.
Answer
Given: A coin is tossed and there is box which contain 2 red and 3 black balls.
To Find: Write the sample space for the given experiment.
Explanation: when coin is tossed , there are 2 outcome {H, T}
According to question, If tail turned up, the a ball is drawn from a box.
So, Sample for This experiment S
1
 = {(T, R
1
)(T, R
2
)(T, B
1
)(T, B
2
)(T, B
3
)}
Now, If Head is turned up, then die is rolled
So, Sample space for this experiment S
2
={(H, 1)(H, 2)(H, 3)(H, 4)(H, 5)(H, 6)}
The required sample space will be S = S
1
  S
2
So, S={(T, R
1
), (T, R
2
), (T, B
1
), (T, B
2
), (T, B
3
), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
Hence, S is the elementary events associated with the given experiment.
12. Question
A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this
experiment.
Answer
Given: A coin is tossed repeatedly until comes up fro the first time.
To Find: Write the sample space for the given experiment.
Explanation: In the given Experiment, a coin is tossed and if the outcome is tail the experiment is over ,
And, if the outcome is Head then the coin is tossed again.
In the second toss also if the outcome is tail then experiment is over, otherwise coin is tossed again.
This process continues indefinitely
SO, The sample space for this experiment is
S={T, HT, HHT, HHHT, HHHHT…}
Hence, S is th sample space for the given experiment.
13. Question
A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement.
Write the sample space for this experiment.
Answer
Given: A box contains 1 red and 3 black balls.
To Find: Write the sample space for the given experiment.
Explanation: We have 1 red and 3 black balls in a box.
Let Assume Red = R
Let Assume Blue = B
Since, two balls are drawn at random without replacement,
So, The sample spaces for this experiment is:
S={(R, B
1
), (R, B
2
), (R, B
3
)(B
1
, B
2
)(B
1
, B
3
)(B
1
, R)(B
2
, R)(B
2
, B
1
)(B
2
, B
3
)(B
3
, R)(B
3
, B
1
)(B
3
, B
2
)}
Hence, S is the sample spaces for given experiment.
14. Question
A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of
elementary events associated to this experiment.
Answer
Given: A pair of dice is rolled , a coin is tossed.
To Find: Write the sample space for the given experiment.
Explanation: A pair of dice is rolled,
Then, No. of elementary events are 6
2
=36
Now, If outcomes is doublet means (1, 1)(2, 2)(3, 3)(4, 4)(5, 5)(6, 6), then a coin is tossed.
If coin is tossed then no. of sample spaces is 2
So, The total no. of elementary events including doublet = 6×2=12
Thus, The Total number of elementary events are 30+12 =42
Hence, 42 events will occur for this experiments.
15. Question
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this
experiment.
Answer
Given: There is a coin which tossed twice.
To Find: Write the sample space for the given experiment.
Explanation: A coin is tossed twice , So the outcomes are
S
1
={HH, HT, TH, TT}
Now, If the second drawn result is head , the a die is rolled then the elementary events is
S
2
={(HH, 1), (HH, 2)(HH, 3), (HH, 4)(HH, 5), (HH, 6), (HH, 1), (TH, 2)(TH, 3), (TH, 4)(TH, 5), (TH, 6)}
Thus, The total sample space for the experiment is S=S
1
 S
2
S={(HH), (HT), (TH), (TT)(HH, 1), (HH, 2)(HH, 3), (HH, 4)(HH, 5), (HH, 6), (HH, 1), (TH, 2)(TH, 3), (TH, 4)(TH,
5), (TH, 6)}
Hence, S is the sample space for given experiment.
16. Question
A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball,
then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?
Answer
Given: A bag contains 4 identical red balls and 3 identical black balls.
To Find: Write the sample space for the given experiment.
Explanation: A bag contains 4 red balls and 3 black balls.
Let us Assume Red = R