This Article consist of most important ” Probability Questions and Answers ” topic that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.
Probability Questions and Answers
Question : 1 Three unbiased coins are tossed. What is the probability of getting at most two heads?
A. 3/4
B. 1/4
C. 3/8
D. 7/8
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Correct Answer : D
Explanation :
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) = n(E)/n(S) = 7/8
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Question : 2 What is the probability of getting a sum 9 from two throws of a dice?
A. 1/6
B. 1/8
C. 1/9
D. 1/12
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Correct Answer : C
Explanation :
In two throws of a die, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) = n(E)/n(S) = 4/36 = 1/9
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Question : 3 In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A. 1/3
B. 3/4
C. 7/19
D. 8/21
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Correct Answer : A
Explanation :
Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7.
P(E) = n(E)/n(S)= 7/21= 1/3
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Question : 4 Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A. 1/2
B. 2/5
C. 8/15
D. 9/20
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Correct Answer : D
Explanation :
Here, S = {1, 2, 3, 4, …., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20
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Question : 5 A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A. 10/21
B. 11/21
C. 2/7
D. 5/7
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Correct Answer : A
Explanation :
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)= Number of ways of drawing 2 balls out of 7
=
7C2 = (7 x 6)/(2 x 1) = 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)= Number of ways of drawing 2 balls out of (2 + 3) balls.
=
5C2
= (5 x 4)/(2 x 1)
= 10.
P(E) = n(E)/n(S) =10/ 21
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