Probability Quiz For All Bank Exams

1. A box contains 27 marbles some are blue and others are green. If a marble is drawn at random from the box, the probability that it is blue is 1/3. Then how many number of green marbles in the box?

A. 10
B. 15
C. 14
D. 18
E. None

Sol. Blue marble – x
xc1/27c1 = 1/3
x/27=1/3 —> x=27/3=9
No of green marbles = Total – Blue marble =27-9=18

2. In a bag there are 4 white, 4 red and 2 green balls. Two balls are drawn at random.What is the probability that at least one ball is of red colour?

A. 4/3
B. 7/3
C. 1/3
D. 2/3
E. None

Sol. Total Balls =10
Other than red ball = 6c2
6c2/10c2=1/3 —> 1-1/3 = 2/3

3. Sahil has two bags (A & B) that contain green and blue balls.In the Bag ‘A’ there are 6 green and 8 blue balls and in the Bag ‘B’ there are 6 green and 6 blue balls. One ball is drawn out from any of these two bags. What is the probability that the ball drawn is blue?

A. 15/28
B. 13/28
C. 17/28
D. 23/28
E. None

Sol. Total balls in A bag = 14, Total balls in A bag = 12
A bag = 1/2(8c1/14c1) = 2/7
B bag = 1/2(6c1/12c1) = 1/4 —> total Probability = 2/7 + 1/4 =15/28

4. In an examination, there are three sections namely Reasoning, Maths and English. Reasoning part contains 4 questions. There are 5 questions in maths section and 6 questions in English section. If three questions are selected randomly from the list of questions then what is the probability that all of them are from maths?

A. 7/91
B. 8/91
C. 2/91
D. 4/91
E. None

Sol. Total no of questions= 15
Probability = 5c3/15c3 = 2/91

5. A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that either all are green or all are red ?

A. 1/20
B. 7/20
C. 3/20
D. 9/20
E. None

Sol. Total Marbles = 12
Either all are green or all are red = 5c3 + 3c3
probability = 5c3 + 3c3/12c3 = 11/220 = 1/20.

6. A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that at least one is blue?

A. 41/55
B. 53/55
C. 47/55
D. 49/55
E. None

Sol. Total Marbles = 12
other than blue 8c3 / 12c3 = 14/55
probability = 1-14/55 = 41/55.

7. A basket contains 5 red 4 blue 3 green marbles. If two marbles picked up random, What is the probability that both are red?

A. 4/33
B. 5/33
C. 7/33
D. 8/33
E. None

Sol. Total Marbles = 12
Probability = 5c2 / 12c2 = 5/33.

8. A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps.If three caps are picked at random, what is the probability that two are red and one is green?

A. 22/55
B. 15/81
C. 10/91
D. 5/91
E. None

Sol. Total caps = 14
Probability = 5c2 * 2c1/ 14c3 = 5/91

9. A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If four caps are picked at random, what is the probability that two are red, one is blue and one is green?

A. 22/1001
B. 80/1001
C. 21/1001
D. 55/1001
E. None

Sol. Total caps = 14
Probability = 5c2 * 4c1 * 2c1 / 14c4 = 80/1001.

10. A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps. If three caps are picked at random, what is the probability that none is green?

A. 2/13
B. 3/13
C. 1/13
D. 5/13
E. None

Sol. Total caps = 14
Probability = 5c0 * 9c3/ 14c3 = 3/13.

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