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Page 1
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
(4) NCERT text book page 386 question no. 4 (*)
(5) NCERT text book page 386 question no. 5 (*)
(6) NCERT text book page 386 question no. 11 (*)
(7) NCERT text book page 386 question no.12 (**)
Type- II
Concept : types of events
(1)NCERT text book page 393 question no. 2 (*)
(2) NCERT text book page 393 question no. 3 (*)
(3) NCERT text book page 393 question no. 1 (*)
(4) NCERT text book page 393 question no. 4 (**)
(5) NCERT text book page 392 example 7 (**)
Type- III
Concept : Algebra of events: AUB , A B , A but not B etc
(1) NCERT text book page 393 question no. 6 (**)
Page 2
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
(4) NCERT text book page 386 question no. 4 (*)
(5) NCERT text book page 386 question no. 5 (*)
(6) NCERT text book page 386 question no. 11 (*)
(7) NCERT text book page 386 question no.12 (**)
Type- II
Concept : types of events
(1)NCERT text book page 393 question no. 2 (*)
(2) NCERT text book page 393 question no. 3 (*)
(3) NCERT text book page 393 question no. 1 (*)
(4) NCERT text book page 393 question no. 4 (**)
(5) NCERT text book page 392 example 7 (**)
Type- III
Concept : Algebra of events: AUB , A B , A but not B etc
(1) NCERT text book page 393 question no. 6 (**)
EXTRA AND HOT QUESTIONS
(1) From a group of 2 men and 3 women 2 persons are selected .
Describe the sample space of the experiment. If E is the event in which 1
man and 1 woman are selected. Then which are the cases favourable to
E (Type-I*)
(2) Two dice are rolled. A is the event that the sum of the numbers shown
on the two dice is 5.B is the event that at least one of the dice shows up
a 3.Are the two events A and B.
(a) Mutually exclusive.
(b) Exhaustive (Type-II**)
(3) Two dice are thrown the events A , B, C are as follows
A: Getting an odd number on the first die.
B: Getting a total of 7 on the two dice.
C: Getting a total of greater than or equal to 8 on the two dice.
Describe the following events
(a) AUB
(b) A’
(c) B – C
(d) B C
PROBABILITY OF AN EVENT
Important concepts
P(E) =
If A and B are two mutually exclusive events P (AUB) = P(A) + P(B)
If A and B are any two events then P (AUB) = P(A) + P(B)-- P(A B)
P(not A) = 1—P(A)
Page 3
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
(4) NCERT text book page 386 question no. 4 (*)
(5) NCERT text book page 386 question no. 5 (*)
(6) NCERT text book page 386 question no. 11 (*)
(7) NCERT text book page 386 question no.12 (**)
Type- II
Concept : types of events
(1)NCERT text book page 393 question no. 2 (*)
(2) NCERT text book page 393 question no. 3 (*)
(3) NCERT text book page 393 question no. 1 (*)
(4) NCERT text book page 393 question no. 4 (**)
(5) NCERT text book page 392 example 7 (**)
Type- III
Concept : Algebra of events: AUB , A B , A but not B etc
(1) NCERT text book page 393 question no. 6 (**)
EXTRA AND HOT QUESTIONS
(1) From a group of 2 men and 3 women 2 persons are selected .
Describe the sample space of the experiment. If E is the event in which 1
man and 1 woman are selected. Then which are the cases favourable to
E (Type-I*)
(2) Two dice are rolled. A is the event that the sum of the numbers shown
on the two dice is 5.B is the event that at least one of the dice shows up
a 3.Are the two events A and B.
(a) Mutually exclusive.
(b) Exhaustive (Type-II**)
(3) Two dice are thrown the events A , B, C are as follows
A: Getting an odd number on the first die.
B: Getting a total of 7 on the two dice.
C: Getting a total of greater than or equal to 8 on the two dice.
Describe the following events
(a) AUB
(b) A’
(c) B – C
(d) B C
PROBABILITY OF AN EVENT
Important concepts
P(E) =
If A and B are two mutually exclusive events P (AUB) = P(A) + P(B)
If A and B are any two events then P (AUB) = P(A) + P(B)-- P(A B)
P(not A) = 1—P(A)
Type – I
Concept: Probability of an event
(1) N.C.E.R.T text book page 404 question no.3(*)
(2) N.C.E.R.T text book page 404 question no.4(**)
(3) N.C.E.R.T text book page 404 question no.8(**)
(4) N.C.E.R.T text book page 404 question no.10(**)
(5) N.C.E.R.T text book page 403 example 14(**)
(6) N.C.E.R.T text book page 400 example 10(**)
EXTRA AND HOT QUESTIONS
(7) Three identical dice are rolled . Find the probability that the same
number will appear on each of them.
Ans: 1/36 (hot)
(8) Two dice are thrown simultaneously . Find the probability of getting a
total of 9.
Ans: 1/9 (*)
(9) A bag contains 8 red ,3 white and 9 blue balls. Three balls are drawn at
random from the bag. Determine the probability that none of the balls
drawn is white .
Ans: 34/57 (**)
(10) In a single throw of 3 dice. Find the probability of not getting the same
number on all the dice.
Ans: 35/36 (**)
(11) The letters of the word “SOCIETY “ are placed at random in a row .What
is the probability that the 3 vowels come together.
Ans: 1/7 (**)
(12) Find the probability that in an arrangement of the letters of the word
“DAUGHTER” the letter D occupies the first place.
Ans: 1/8 (**)
(13) Find the probability that in a random arrangement of the letters of the
word “INSTITUTION’ the three T’s are together.
Ans: P 1/110 (**)
Page 4
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
(4) NCERT text book page 386 question no. 4 (*)
(5) NCERT text book page 386 question no. 5 (*)
(6) NCERT text book page 386 question no. 11 (*)
(7) NCERT text book page 386 question no.12 (**)
Type- II
Concept : types of events
(1)NCERT text book page 393 question no. 2 (*)
(2) NCERT text book page 393 question no. 3 (*)
(3) NCERT text book page 393 question no. 1 (*)
(4) NCERT text book page 393 question no. 4 (**)
(5) NCERT text book page 392 example 7 (**)
Type- III
Concept : Algebra of events: AUB , A B , A but not B etc
(1) NCERT text book page 393 question no. 6 (**)
EXTRA AND HOT QUESTIONS
(1) From a group of 2 men and 3 women 2 persons are selected .
Describe the sample space of the experiment. If E is the event in which 1
man and 1 woman are selected. Then which are the cases favourable to
E (Type-I*)
(2) Two dice are rolled. A is the event that the sum of the numbers shown
on the two dice is 5.B is the event that at least one of the dice shows up
a 3.Are the two events A and B.
(a) Mutually exclusive.
(b) Exhaustive (Type-II**)
(3) Two dice are thrown the events A , B, C are as follows
A: Getting an odd number on the first die.
B: Getting a total of 7 on the two dice.
C: Getting a total of greater than or equal to 8 on the two dice.
Describe the following events
(a) AUB
(b) A’
(c) B – C
(d) B C
PROBABILITY OF AN EVENT
Important concepts
P(E) =
If A and B are two mutually exclusive events P (AUB) = P(A) + P(B)
If A and B are any two events then P (AUB) = P(A) + P(B)-- P(A B)
P(not A) = 1—P(A)
Type – I
Concept: Probability of an event
(1) N.C.E.R.T text book page 404 question no.3(*)
(2) N.C.E.R.T text book page 404 question no.4(**)
(3) N.C.E.R.T text book page 404 question no.8(**)
(4) N.C.E.R.T text book page 404 question no.10(**)
(5) N.C.E.R.T text book page 403 example 14(**)
(6) N.C.E.R.T text book page 400 example 10(**)
EXTRA AND HOT QUESTIONS
(7) Three identical dice are rolled . Find the probability that the same
number will appear on each of them.
Ans: 1/36 (hot)
(8) Two dice are thrown simultaneously . Find the probability of getting a
total of 9.
Ans: 1/9 (*)
(9) A bag contains 8 red ,3 white and 9 blue balls. Three balls are drawn at
random from the bag. Determine the probability that none of the balls
drawn is white .
Ans: 34/57 (**)
(10) In a single throw of 3 dice. Find the probability of not getting the same
number on all the dice.
Ans: 35/36 (**)
(11) The letters of the word “SOCIETY “ are placed at random in a row .What
is the probability that the 3 vowels come together.
Ans: 1/7 (**)
(12) Find the probability that in an arrangement of the letters of the word
“DAUGHTER” the letter D occupies the first place.
Ans: 1/8 (**)
(13) Find the probability that in a random arrangement of the letters of the
word “INSTITUTION’ the three T’s are together.
Ans: P 1/110 (**)
Type – II
P(AUB)= P(A) + P(B) (mutually exclusive cases )
P (AUB) = P(A) + P(B)-- P(A B)
(1) N.C.E.R.T page 405 question no.14(**)
(2) N.C.E.R.T page 405 question no.15(*)
(3) N.C.E.R.T page 405 question no.16(**)
(4) N.C.E.R.T page 405 question no.17(**)
(5) N.C.E.R.T page 405 question no.18(**)
(6) N.C.E.R.T page 405 question no.19(**)
(7) N.C.E.R.T page 405 question no.20 (**)
(8) N.C.E.R.T page 409 misc exercise question no.3 (**)
(9) N.C.E.R.T page 401 example 11(**)
EXTRA AND HOT QUESTIONS
(1) One card is drawn from a set of 17 cards numbered 1 to 17. Find the
probability that the number is divisible by 3 or 7.
Ans: 7/17. (*)
(2) Two dice are thrown together. What is the probability that the sum of
the numbers of the two faces is neither 9 nor 11.
Ans : 5/16 (*)
(3) Two unbiased dice are thrown. Find the probability that neither a
doublet nor a total of 10 will appear.
Ans: 7/9 (**)
(4) Two cards are drawn from a well shuffled pack of 52 cards without
replacement .Find the probability that neither a jack nor a card of
spade is drawn.
Ans: 105/221 (**)
(5) If P(AUB)=0.6 and P(A B)=0.2. Find P(
¯
) + P(
¯
)
Ans: 1.2
Page 5
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
(4) NCERT text book page 386 question no. 4 (*)
(5) NCERT text book page 386 question no. 5 (*)
(6) NCERT text book page 386 question no. 11 (*)
(7) NCERT text book page 386 question no.12 (**)
Type- II
Concept : types of events
(1)NCERT text book page 393 question no. 2 (*)
(2) NCERT text book page 393 question no. 3 (*)
(3) NCERT text book page 393 question no. 1 (*)
(4) NCERT text book page 393 question no. 4 (**)
(5) NCERT text book page 392 example 7 (**)
Type- III
Concept : Algebra of events: AUB , A B , A but not B etc
(1) NCERT text book page 393 question no. 6 (**)
EXTRA AND HOT QUESTIONS
(1) From a group of 2 men and 3 women 2 persons are selected .
Describe the sample space of the experiment. If E is the event in which 1
man and 1 woman are selected. Then which are the cases favourable to
E (Type-I*)
(2) Two dice are rolled. A is the event that the sum of the numbers shown
on the two dice is 5.B is the event that at least one of the dice shows up
a 3.Are the two events A and B.
(a) Mutually exclusive.
(b) Exhaustive (Type-II**)
(3) Two dice are thrown the events A , B, C are as follows
A: Getting an odd number on the first die.
B: Getting a total of 7 on the two dice.
C: Getting a total of greater than or equal to 8 on the two dice.
Describe the following events
(a) AUB
(b) A’
(c) B – C
(d) B C
PROBABILITY OF AN EVENT
Important concepts
P(E) =
If A and B are two mutually exclusive events P (AUB) = P(A) + P(B)
If A and B are any two events then P (AUB) = P(A) + P(B)-- P(A B)
P(not A) = 1—P(A)
Type – I
Concept: Probability of an event
(1) N.C.E.R.T text book page 404 question no.3(*)
(2) N.C.E.R.T text book page 404 question no.4(**)
(3) N.C.E.R.T text book page 404 question no.8(**)
(4) N.C.E.R.T text book page 404 question no.10(**)
(5) N.C.E.R.T text book page 403 example 14(**)
(6) N.C.E.R.T text book page 400 example 10(**)
EXTRA AND HOT QUESTIONS
(7) Three identical dice are rolled . Find the probability that the same
number will appear on each of them.
Ans: 1/36 (hot)
(8) Two dice are thrown simultaneously . Find the probability of getting a
total of 9.
Ans: 1/9 (*)
(9) A bag contains 8 red ,3 white and 9 blue balls. Three balls are drawn at
random from the bag. Determine the probability that none of the balls
drawn is white .
Ans: 34/57 (**)
(10) In a single throw of 3 dice. Find the probability of not getting the same
number on all the dice.
Ans: 35/36 (**)
(11) The letters of the word “SOCIETY “ are placed at random in a row .What
is the probability that the 3 vowels come together.
Ans: 1/7 (**)
(12) Find the probability that in an arrangement of the letters of the word
“DAUGHTER” the letter D occupies the first place.
Ans: 1/8 (**)
(13) Find the probability that in a random arrangement of the letters of the
word “INSTITUTION’ the three T’s are together.
Ans: P 1/110 (**)
Type – II
P(AUB)= P(A) + P(B) (mutually exclusive cases )
P (AUB) = P(A) + P(B)-- P(A B)
(1) N.C.E.R.T page 405 question no.14(**)
(2) N.C.E.R.T page 405 question no.15(*)
(3) N.C.E.R.T page 405 question no.16(**)
(4) N.C.E.R.T page 405 question no.17(**)
(5) N.C.E.R.T page 405 question no.18(**)
(6) N.C.E.R.T page 405 question no.19(**)
(7) N.C.E.R.T page 405 question no.20 (**)
(8) N.C.E.R.T page 409 misc exercise question no.3 (**)
(9) N.C.E.R.T page 401 example 11(**)
EXTRA AND HOT QUESTIONS
(1) One card is drawn from a set of 17 cards numbered 1 to 17. Find the
probability that the number is divisible by 3 or 7.
Ans: 7/17. (*)
(2) Two dice are thrown together. What is the probability that the sum of
the numbers of the two faces is neither 9 nor 11.
Ans : 5/16 (*)
(3) Two unbiased dice are thrown. Find the probability that neither a
doublet nor a total of 10 will appear.
Ans: 7/9 (**)
(4) Two cards are drawn from a well shuffled pack of 52 cards without
replacement .Find the probability that neither a jack nor a card of
spade is drawn.
Ans: 105/221 (**)
(5) If P(AUB)=0.6 and P(A B)=0.2. Find P(
¯
) + P(
¯
)
Ans: 1.2
(6) A and B are two mutually exclusive events if P(A) = 0.5 and P(
¯
)
=0.6.Find P(AUB)
Type – III
At least one, at most one cases
(1) N.C.E.R.T page 402 examples 12 (**) {hot}
(2) N.C.E.R.T page 407 example 15 (**)
(3) N.C.E.R.T page 408 misc exercise question .1 (**) {hot}
(4) N.C.E.R.T page 408 misc exercise question.2 (**)
(5) N.C.E.R.T page 409 misc exercise question 7 (**)
(6) N.C.E.R.T page 409 misc exercise question 9 (**)
EXTRA AND HOT QUESTIONS
(1) Three coins are tossed once . Find the probability of getting
(a) Atmost 2 heads
(b) Atleast 2 heads
(c) Exactly 2 tails
(d) Atmost 2 tails
(e) 3 heads
(f) No heads
Ans: (a) 7/8 (b)1/2 (c)3/8 (d)7/8 (e)1/8 (f)1/8
(2) The probability that a student will get A,B,C or D grade are
0.4,0.35,0.15and 0.1 respectively. Find the probability that she will get
(a) B or C grade
(b) Atmost C grade
(3) In a single throw of 2 dice write the corresponding events and the
probability of getting
(a) A total of 9
(b) Two ones
(c) Atleast one 6
(d) A sum of 9 or 11
(e) A sum of atleast 10
(f) A sum as a prime number
Ans: (a)1/9(b)1/36(c)11/36(d)1/6(e)1/6(f)5/12
Read More
FAQs on Probability Notes - Class 11
| 1. What is probability in mathematics? |  |
Ans. Probability is a branch of mathematics that deals with the study of uncertainty and the likelihood of events occurring. It quantifies the chances of an event happening by assigning a numerical value between 0 and 1, where 0 represents impossibility and 1 represents certainty.
| 2. How is probability calculated? | |
Ans. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability formula: P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
| 3. What are the different types of probability? | |
Ans. There are three types of probability:
1. Classical Probability: It is based on equally likely outcomes and is used when all possible outcomes are equally likely to occur.
2. Empirical Probability: It is based on observed data or experiments. The probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.
3. Subjective Probability: It is based on personal judgment or opinions. It is used when there is no historical data or experimental evidence available.
| 4. How can probability be used in real-life situations? | |
Ans. Probability is used in various real-life situations, including:
1. Weather Forecasting: Meteorologists use probability to predict the chances of rain, snow, or other weather conditions.
2. Gambling: Probability is used to determine the odds of winning in games of chance, such as card games or lotteries.
3. Insurance: Insurance companies use probability to assess risks and calculate premiums for different types of insurance policies.
4. Medical Diagnosis: Probability is used in medical diagnosis to assess the likelihood of a disease based on symptoms, test results, and patient history.
| 5. What is conditional probability? | |
Ans. Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are two events. The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events A and B occurring together, and P(B) is the probability of event B occurring. Conditional probability is used to determine the likelihood of an event happening under certain conditions or assumptions.
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Nov 24, 2024 Last updated |
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