Probability - Exercise 25A | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
i
A coin is tossed. What are all possible outcomes?
ii
Two coins are tossed simultaneously. What are all possible outcomes?
iii
A die is thrown. What are all possible outcomes?
iv
From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
S o l u t i o n :
i
The possible outcomes are head (H) and tail (T).
ii
The possible outcomes are HH, HT, TH and TT.
iii
The possible outcomes are 1, 2, 3, 4, 5 and 6.
iv
The total number of possible outcomes is 52.
Q u e s t i o n : 2
In a single throw of a coin, what is the probability of getting a tail?
S o l u t i o n :
The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
? P
(tail)
=
1
2
Q u e s t i o n : 3
In a single throw of two coins, find the probability of getting
i
both tails,
ii
at least 1 tail,
iii
at the most 1 tail.
S o l u t i o n :
The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4
i
Getting both tails means TT.
Number of outcomes with two tails = 1
? P
(both tails)
=
1
4
 
ii
Getting at least 1 tail means HT, TH and TT.
?With at least one tail, total number of outcomes = 3
? P
(at least 1 tail)
=
3
4
Page 2


Q u e s t i o n : 1
i
A coin is tossed. What are all possible outcomes?
ii
Two coins are tossed simultaneously. What are all possible outcomes?
iii
A die is thrown. What are all possible outcomes?
iv
From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
S o l u t i o n :
i
The possible outcomes are head (H) and tail (T).
ii
The possible outcomes are HH, HT, TH and TT.
iii
The possible outcomes are 1, 2, 3, 4, 5 and 6.
iv
The total number of possible outcomes is 52.
Q u e s t i o n : 2
In a single throw of a coin, what is the probability of getting a tail?
S o l u t i o n :
The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
? P
(tail)
=
1
2
Q u e s t i o n : 3
In a single throw of two coins, find the probability of getting
i
both tails,
ii
at least 1 tail,
iii
at the most 1 tail.
S o l u t i o n :
The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4
i
Getting both tails means TT.
Number of outcomes with two tails = 1
? P
(both tails)
=
1
4
 
ii
Getting at least 1 tail means HT, TH and TT.
?With at least one tail, total number of outcomes = 3
? P
(at least 1 tail)
=
3
4
iii
Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
? ?P
(at most 1 tail)
=
3
4
Q u e s t i o n : 4
A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the
probability of getting
i
a white ball?
ii
a blue ball?
S o l u t i o n :
Total number of balls = 4 +5 = 9
i
Number of white balls = 4
? ? P
(white ball)
=
4
9
Number of blue balls = 5
? ? P
(blue ball)
=
5
9
Q u e s t i o n : 5
A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball
drawn is
i
green?
ii
white?
iii
non-red?
S o l u t i o n :
Total number of balls = 5 +6 +4 = 15
i
Number of green balls = 4
? ? P
(green ball)
=
4
15
ii
Number of white balls = 5
? ? P
(white ball)
=
5
15
=
1
3
iii
Number of balls that are not red i. e. , 5whiteand4green
= 9
? ? P
(non-red balls)
=
9
15
=
3
5
Page 3


Q u e s t i o n : 1
i
A coin is tossed. What are all possible outcomes?
ii
Two coins are tossed simultaneously. What are all possible outcomes?
iii
A die is thrown. What are all possible outcomes?
iv
From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
S o l u t i o n :
i
The possible outcomes are head (H) and tail (T).
ii
The possible outcomes are HH, HT, TH and TT.
iii
The possible outcomes are 1, 2, 3, 4, 5 and 6.
iv
The total number of possible outcomes is 52.
Q u e s t i o n : 2
In a single throw of a coin, what is the probability of getting a tail?
S o l u t i o n :
The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
? P
(tail)
=
1
2
Q u e s t i o n : 3
In a single throw of two coins, find the probability of getting
i
both tails,
ii
at least 1 tail,
iii
at the most 1 tail.
S o l u t i o n :
The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4
i
Getting both tails means TT.
Number of outcomes with two tails = 1
? P
(both tails)
=
1
4
 
ii
Getting at least 1 tail means HT, TH and TT.
?With at least one tail, total number of outcomes = 3
? P
(at least 1 tail)
=
3
4
iii
Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
? ?P
(at most 1 tail)
=
3
4
Q u e s t i o n : 4
A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the
probability of getting
i
a white ball?
ii
a blue ball?
S o l u t i o n :
Total number of balls = 4 +5 = 9
i
Number of white balls = 4
? ? P
(white ball)
=
4
9
Number of blue balls = 5
? ? P
(blue ball)
=
5
9
Q u e s t i o n : 5
A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball
drawn is
i
green?
ii
white?
iii
non-red?
S o l u t i o n :
Total number of balls = 5 +6 +4 = 15
i
Number of green balls = 4
? ? P
(green ball)
=
4
15
ii
Number of white balls = 5
? ? P
(white ball)
=
5
15
=
1
3
iii
Number of balls that are not red i. e. , 5whiteand4green
= 9
? ? P
(non-red balls)
=
9
15
=
3
5
Q u e s t i o n : 6
In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a
prize?
S o l u t i o n :
Total number of tickets = 10 +20 = 30
Number of prize tickets = 10
? ? P
(getting a prize)
=
10
30
=
1
3
Q u e s t i o n : 7
It is known that a box of 100 electric bulbs contains 8 defective bulbs. One bulb is taken out at random from the
box. What is the probability that the bulb drawn is
i
defective?
ii
non-defective?
S o l u t i o n :
Total number of bulbs in the box = 100
i
Number of defective bulbs = 8
? ? P
(defective bulb)
=
8
100
=
2
25
ii
Number of functioning bulbs= 100 -8 = 92
? ? P
(non-defective bulb)
=
92
100
=
23
25
Q u e s t i o n : 8
A die is thrown at random. Find the probability of getting
i
2
ii
a number less than 3
iii
a composite number
iv
a number not less than 4.
S o l u t i o n :
The possible outcomes when a dice is thrown at random are 1, 2, 3, 4, 5 and 6.
Total number of outcomes = 6
i
? ? P
(getting 2)
=
1
6
ii
The numbers less than 3 are 1 and 2.
      Number of possible outcomes = 2
Page 4


Q u e s t i o n : 1
i
A coin is tossed. What are all possible outcomes?
ii
Two coins are tossed simultaneously. What are all possible outcomes?
iii
A die is thrown. What are all possible outcomes?
iv
From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
S o l u t i o n :
i
The possible outcomes are head (H) and tail (T).
ii
The possible outcomes are HH, HT, TH and TT.
iii
The possible outcomes are 1, 2, 3, 4, 5 and 6.
iv
The total number of possible outcomes is 52.
Q u e s t i o n : 2
In a single throw of a coin, what is the probability of getting a tail?
S o l u t i o n :
The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
? P
(tail)
=
1
2
Q u e s t i o n : 3
In a single throw of two coins, find the probability of getting
i
both tails,
ii
at least 1 tail,
iii
at the most 1 tail.
S o l u t i o n :
The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4
i
Getting both tails means TT.
Number of outcomes with two tails = 1
? P
(both tails)
=
1
4
 
ii
Getting at least 1 tail means HT, TH and TT.
?With at least one tail, total number of outcomes = 3
? P
(at least 1 tail)
=
3
4
iii
Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
? ?P
(at most 1 tail)
=
3
4
Q u e s t i o n : 4
A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the
probability of getting
i
a white ball?
ii
a blue ball?
S o l u t i o n :
Total number of balls = 4 +5 = 9
i
Number of white balls = 4
? ? P
(white ball)
=
4
9
Number of blue balls = 5
? ? P
(blue ball)
=
5
9
Q u e s t i o n : 5
A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball
drawn is
i
green?
ii
white?
iii
non-red?
S o l u t i o n :
Total number of balls = 5 +6 +4 = 15
i
Number of green balls = 4
? ? P
(green ball)
=
4
15
ii
Number of white balls = 5
? ? P
(white ball)
=
5
15
=
1
3
iii
Number of balls that are not red i. e. , 5whiteand4green
= 9
? ? P
(non-red balls)
=
9
15
=
3
5
Q u e s t i o n : 6
In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a
prize?
S o l u t i o n :
Total number of tickets = 10 +20 = 30
Number of prize tickets = 10
? ? P
(getting a prize)
=
10
30
=
1
3
Q u e s t i o n : 7
It is known that a box of 100 electric bulbs contains 8 defective bulbs. One bulb is taken out at random from the
box. What is the probability that the bulb drawn is
i
defective?
ii
non-defective?
S o l u t i o n :
Total number of bulbs in the box = 100
i
Number of defective bulbs = 8
? ? P
(defective bulb)
=
8
100
=
2
25
ii
Number of functioning bulbs= 100 -8 = 92
? ? P
(non-defective bulb)
=
92
100
=
23
25
Q u e s t i o n : 8
A die is thrown at random. Find the probability of getting
i
2
ii
a number less than 3
iii
a composite number
iv
a number not less than 4.
S o l u t i o n :
The possible outcomes when a dice is thrown at random are 1, 2, 3, 4, 5 and 6.
Total number of outcomes = 6
i
? ? P
(getting 2)
=
1
6
ii
The numbers less than 3 are 1 and 2.
      Number of possible outcomes = 2
      ? ? P
(getting a number<3)
=
2
6
=
1
3
iii
A composite number is defined as a number with at least one positive divisor other than itself and unity.
In a dice, 4 and 6 are composite numbers.
Number of possible outcomes = 2
? ? P
(getting a composite number)
=
2
6
=
1
3
 
iv
A number not less than 4 can includes 4, 5 or 6.
      Number of outcomes = 3  
      ?P
(getting a number not less than 4)
=
3
6
=
1
2
Q u e s t i o n : 9
In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at
random. What is the probability that the chosen lady dislikes coffee?
S o l u t i o n :
Total number of ladies surveyed = 200
Number of ladies who dislike coffee = 118
If chosen randomly, P
(a lady that dislikes coffee)
 = 
118
200
=
59
100
Q u e s t i o n : 1 0
A box contains 19 balls bearing numbers 1, 2, 3, ..., 19 respectively. A ball is drawn at random from the box. Find
the probability that the number on the ball is
i
a prime number
ii
an even number
iii
a number divisible by 3.
S o l u t i o n :
Total number of possible outcomes = 19
i
The prime numbers between 1 and 19 are 2, 3, 5, 7, 11, 13, 17 and 19.
     Total number of primes = 8
   
     ? P
(prime number)
=
8
19
ii
The even numbers between 1 and 19 are 2, 4, 6, 8, 10 ,12, 14, 16 and 18.
      Total number of even numbers = 6
     ? P
(even number)
=
9
19
iii
Page 5


Q u e s t i o n : 1
i
A coin is tossed. What are all possible outcomes?
ii
Two coins are tossed simultaneously. What are all possible outcomes?
iii
A die is thrown. What are all possible outcomes?
iv
From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
S o l u t i o n :
i
The possible outcomes are head (H) and tail (T).
ii
The possible outcomes are HH, HT, TH and TT.
iii
The possible outcomes are 1, 2, 3, 4, 5 and 6.
iv
The total number of possible outcomes is 52.
Q u e s t i o n : 2
In a single throw of a coin, what is the probability of getting a tail?
S o l u t i o n :
The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
? P
(tail)
=
1
2
Q u e s t i o n : 3
In a single throw of two coins, find the probability of getting
i
both tails,
ii
at least 1 tail,
iii
at the most 1 tail.
S o l u t i o n :
The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4
i
Getting both tails means TT.
Number of outcomes with two tails = 1
? P
(both tails)
=
1
4
 
ii
Getting at least 1 tail means HT, TH and TT.
?With at least one tail, total number of outcomes = 3
? P
(at least 1 tail)
=
3
4
iii
Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
? ?P
(at most 1 tail)
=
3
4
Q u e s t i o n : 4
A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the
probability of getting
i
a white ball?
ii
a blue ball?
S o l u t i o n :
Total number of balls = 4 +5 = 9
i
Number of white balls = 4
? ? P
(white ball)
=
4
9
Number of blue balls = 5
? ? P
(blue ball)
=
5
9
Q u e s t i o n : 5
A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball
drawn is
i
green?
ii
white?
iii
non-red?
S o l u t i o n :
Total number of balls = 5 +6 +4 = 15
i
Number of green balls = 4
? ? P
(green ball)
=
4
15
ii
Number of white balls = 5
? ? P
(white ball)
=
5
15
=
1
3
iii
Number of balls that are not red i. e. , 5whiteand4green
= 9
? ? P
(non-red balls)
=
9
15
=
3
5
Q u e s t i o n : 6
In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a
prize?
S o l u t i o n :
Total number of tickets = 10 +20 = 30
Number of prize tickets = 10
? ? P
(getting a prize)
=
10
30
=
1
3
Q u e s t i o n : 7
It is known that a box of 100 electric bulbs contains 8 defective bulbs. One bulb is taken out at random from the
box. What is the probability that the bulb drawn is
i
defective?
ii
non-defective?
S o l u t i o n :
Total number of bulbs in the box = 100
i
Number of defective bulbs = 8
? ? P
(defective bulb)
=
8
100
=
2
25
ii
Number of functioning bulbs= 100 -8 = 92
? ? P
(non-defective bulb)
=
92
100
=
23
25
Q u e s t i o n : 8
A die is thrown at random. Find the probability of getting
i
2
ii
a number less than 3
iii
a composite number
iv
a number not less than 4.
S o l u t i o n :
The possible outcomes when a dice is thrown at random are 1, 2, 3, 4, 5 and 6.
Total number of outcomes = 6
i
? ? P
(getting 2)
=
1
6
ii
The numbers less than 3 are 1 and 2.
      Number of possible outcomes = 2
      ? ? P
(getting a number<3)
=
2
6
=
1
3
iii
A composite number is defined as a number with at least one positive divisor other than itself and unity.
In a dice, 4 and 6 are composite numbers.
Number of possible outcomes = 2
? ? P
(getting a composite number)
=
2
6
=
1
3
 
iv
A number not less than 4 can includes 4, 5 or 6.
      Number of outcomes = 3  
      ?P
(getting a number not less than 4)
=
3
6
=
1
2
Q u e s t i o n : 9
In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at
random. What is the probability that the chosen lady dislikes coffee?
S o l u t i o n :
Total number of ladies surveyed = 200
Number of ladies who dislike coffee = 118
If chosen randomly, P
(a lady that dislikes coffee)
 = 
118
200
=
59
100
Q u e s t i o n : 1 0
A box contains 19 balls bearing numbers 1, 2, 3, ..., 19 respectively. A ball is drawn at random from the box. Find
the probability that the number on the ball is
i
a prime number
ii
an even number
iii
a number divisible by 3.
S o l u t i o n :
Total number of possible outcomes = 19
i
The prime numbers between 1 and 19 are 2, 3, 5, 7, 11, 13, 17 and 19.
     Total number of primes = 8
   
     ? P
(prime number)
=
8
19
ii
The even numbers between 1 and 19 are 2, 4, 6, 8, 10 ,12, 14, 16 and 18.
      Total number of even numbers = 6
     ? P
(even number)
=
9
19
iii
The numbers between 1 and 19 which are divisible by 3 are 3, 6, 9, 12, 15 and 18.
       Total number of possible outcomes = 6
       ? P
(number divisble by 3)
=
6
19
 
 
 
Q u e s t i o n : 1 1
One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is
i
a king
ii
a spade
iii
a red queen
iv
a black 8.
S o l u t i o n :
Total number of possible outcomes = 52
i
There are 4 kings cards kingofhearts, kingofdiamonds, kingofspadesandkingofcloves
Number of kings = 4
? P
(king)
=
4
52
=
1
13
ii
There is a total of 13 spades cards.
Number of spades = 13
? P
(spades)
=
13
52
=
1
4
iii
There are 2 red queens in a pack queenofheartsandqueenofdiamonds
Number of red queens = 2
? P
(red queen)
=
2
52
=
1
26
 
iv
There are 2 black 8s in a pack 8ofclovesand8ofspades
Number of black 8s = 2
? P
(black 8)
=
2
52
=
1
26
 
 
Q u e s t i o n : 1 2
One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is