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This mock test of Probability - MCQ 4 for Quant helps you for every Quant entrance exam.
This contains 20 Multiple Choice Questions for Quant Probability - MCQ 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

A box contain 4 white, 3 blue and 2 black marbles. If 2 marbles are picked up at random. What is the probability that both of them are black ?

Solution:

P = 2C2/9C2 = 1/36

QUESTION: 2

An urn contains 6 maroon, 3 pink and 4 white balls. If three balls are drawn What is the probability that all are pink or white?

Solution:

P =3C3/13C3 + 4C3/13C3

= 1/286 + 4/286 = 5/286

QUESTION: 3

From a pack of 52 cards 3 cards are drawn one by one without replacements.Find the probability that both of them are king ?

Solution:

4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525

QUESTION: 4

If two dice are thrown simultaneously, what is the probability that the sum of the numbers appeared is less than seven?

Solution:

Sum of the numbers can be 1,2, 3, 4, 5, and 6.

1+2= 3

1+3 = 4

1+4 = 5

1+5 = 6

2+3 = 5

3+2 = 5

2+4 = 6

4+2 = 6……..etc

n (E) = 15, n (S) = 36

P (E) =15/36 = 5/12

QUESTION: 5

A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green ?

Solution:

4C2+(4C1*10C1)/12C2 = 6+40/91 = 46/91

QUESTION: 6

In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK ?

Solution:

P = 6/18 = 1/3

QUESTION: 7

A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?

Solution:

P = 4C1*8C3/12C4 = 4*56/495 = 224/495

QUESTION: 8

A bag contains 4 white, 8 black and 6 blue balls. If two balls are drawn at random, find the probability of both the balls being black?

Solution:

n(S) = 18C2 = 153

There are eight black balls, out of which two balls are drawn in 8C2 ways.

n(E) = 28

P(E) = 28 /153 = 28/153

QUESTION: 9

The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?

Solution:

5:2 = 15+6 = 21

n(S) = 21C3 = 1330

n(E) = 15C1 × 6C2 = 15 × 15 = 225

P = 225/1330 = 45/266

QUESTION: 10

A bag 5 red and 8 white balls.Two draws of three balls each are made.What is the probability that the balls were pink in the first draw and white in the second draw ?

Solution:

5C3/13C3 *8C3/13C3 = 60/286*56/286 = 140/20449

QUESTION: 11

From a pack of 52 cads, 2 cards are drawn at random. What is the probability of drawing such that there is at least 1 king?

Solution:

Case 1: 1 is king

^{4}C_{1} * ^{48}C_{1} / ^{52}C_{2}

Case 2: both are king

^{4}C_{2} / ^{52}C_{2}

Add both cases.

QUESTION: 12

A box contains 6 blue, 5 green and 4 red balls. If two balls are pick at random, then what is the probability that neither is blue?

Solution:

Total balls = 15

Not blue means green or red i.e. any of (5+4) = 9 balls

So prob. = ^{9}C_{2} / ^{15}C_{2}

QUESTION: 13

A box contains 5 blue and 5 white balls. What is the probability of drawing 2 balls such that both are same in color?

Solution:

Case 1: Both blue

^{5}C_{2} / ^{10}C_{2}

Case 2: Both white

^{5}C_{2} / ^{10}C_{2}

Add both cases

QUESTION: 14

A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?

Solution:

2 children should be there and rest 2 either from (2 women + 3 men) 5 people

So prob. = ^{4}C_{2} * ^{5}C_{2} / ^{9}C_{4}

QUESTION: 15

In a class 30% of the students opt for Math, 20% opt for Computers and 10% opt for both. A student is selected at random, find the probability that he has opted either Math or Computers.

Solution:

Prob. of math = 30/100 = 3/10, Prob. of computers = 20/100 = 1/5, prob. for both = 10/100 = 1/10

So required prob. = 3/5 + 1/5 – 1/10

QUESTION: 16

From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?

Solution:

Prob. of both red = ^{26}C_{2} / ^{52}C_{2}

Prob. of both kings = ^{4}C_{2} / ^{52}C_{2}

Since there are also cads which are both red and king, so we will subtract there prob.

There are 2 red cards which are kings

Prob. of both red and king = ^{2}C_{2} / ^{52}C_{2}

So required prob. = ^{26}C_{2} / ^{52}C_{2} + ^{4}C_{2} / ^{52}C_{2} – ^{2}C_{2} / ^{52}C_{2}

QUESTION: 17

A box contains 10 electric bulbs from which 2 bulbs are defective. Two bulbs are chosen at random. What is the probability that one of them is defective?

Solution:

QUESTION: 18

A bag contains 8 blue and 7 green balls. A ball is drawn out of it and put back in the bag. Then a ball is drawn again. What is the probability that both the balls are green?

Solution:

QUESTION: 19

A bag contains 8 blue and 7 green balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are alternately of different colors?

Solution:

When 1st is blue, prob. = 8/15 * 7/14

When 1st is green, prob. = 7/15 * 8/14

Add both cases.

QUESTION: 20

There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.

Solution:

2 men and 1 woman, prob. = ^{5}C_{2} * ^{3}C_{1} / ^{8}C_{3}

2 women and 1 man, prob. = ^{5}C_{1} * ^{3}C_{2} / ^{8}C_{3}

Add both cases

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