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This mock test of Probability - MCQ 3 for Quant helps you for every Quant entrance exam.
This contains 20 Multiple Choice Questions for Quant Probability - MCQ 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

When two coins are tossed simultaneously, what are the chances of getting at least one tail?

Solution:

QUESTION: 2

A bag contains 3 red balls and 8 blacks ball and another bag contains 5 red balls and 7 blacks balls, one ball is drawn at random from either of the bag, find the probability that the ball is red.

Solution:

Probability = probability of selecting the bag and probability of selecting red ball

(1/2)*(3/11) + (1/2)*(5/12) = 91/264

QUESTION: 3

12 persons are seated at a circular table. Find the probability that 3 particular persons always seated together.

Solution:

total probability = (12-1)! = 11!

Desired probability = (10 – 1)! = 9!

So, p = (9! *3!) /11! = 3/55

QUESTION: 4

P and Q are two friends standing in a circular arrangement with 10 more people. Find the probability that exactly 3 persons are seated between P and Q.

Solution:

Fix P at one point then number of places where B can be seated is 11.

Now, exactly three persons can be seated between P and Q, so only two places where Q can be seated. So, p = 2/11

QUESTION: 5

A basket contains 5 black and 8 yellow balls. Four balls are drawn at random and not replaced. What is the probability that they are of different colours alternatively.

Solution:

sol⇒ BYBY + YBYB = (5/13)*(8/12)*(4/11)*(7/10) + (8/13)*(5/12)*(7/11)*(4/10)

= 56/429

QUESTION: 6

Direction(Q6 – Q8):

A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

**Q. **

**Both the balls are green**

Solution:

P = (8/14)*(8/14)

QUESTION: 7

A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

**Q. **

**First one is green and second one is red **

Solution:

P = (8/14)*(6/14)

QUESTION: 8

A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

**Q. **

**Both the balls are red**

Solution:

P = (6/14)*(6/14)

QUESTION: 9

Find the probability that in a leap year, the numbers of Mondays are 53?

Solution:

In a leap year there are 52 complete weeks i.e. 364 days and 2 more days. These 2 days can be SM, MT, TW, WT, TF, FS, and SS.

So P = 2/7

QUESTION: 10

A urn contains 4 red balls, 5 green balls and 6 white balls, if one ball is drawn at random, find the probability that it is neither red nor white.

Solution:

5c1/15c1 = 1/3

QUESTION: 11

A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?

Solution:

From 1 to 24, there are 8 numbers which are multiple of 3

Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets

^{8}C_{2} * ^{16}C_{1} / ^{24}C_{3} = 56/253

Case 2: all are multiples of 3.

^{8}C_{3} / ^{24}C_{3} = 7/253

Add both cases.

QUESTION: 12

A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?

Solution:

Total balls = 15

Not red means green or blue i.e. any of (5+6) = 11 balls

So prob. = ^{11}C_{2} / ^{15}C_{2}

QUESTION: 13

From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or heart card?

Solution:

Prob. of black card:

^{26}C_{2} / ^{52}C_{2} = 25/102

Prob. of heart card:

^{13}C_{2} / ^{52}C_{2} = 3/51

Add both cases.

QUESTION: 14

Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?

Solution:

There are total 26 cards black, and 4 jacks in which 2 are black jacks

So case 1: both are black

^{26}C_{2} / ^{52}C_{2}

case 2: both are jack

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

Add both cases.

But now 2 black jacks have been added in both cases, so subtracting their prob. :

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

So 325/1326 + 6/1326 – 1/1326

QUESTION: 15

From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?

Solution:

Case 1: Prob. when 2 men, 1 woman and 1 child

^{3}C_{2} * ^{4}C_{1} * ^{2}C_{1} / ^{9}C_{4} = 4/21

Case 2: Prob. when 1 man, 2 women and 1 child

^{3}C_{1} * ^{4}C_{1} * ^{2}C_{1} / ^{9}C_{4} = 2/7

Case 3: Prob. when 1 man, 1 woman and 2 children

^{3}C_{1} * ^{4}C_{1} * ^{2}C_{2} / ^{9}C_{4} = 2/21

QUESTION: 16

A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?

Solution:

QUESTION: 17

There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?

Solution:

Case 1: 0 green ball means all three red or white balls

^{9}C_{3} / ^{12}C_{3}

Case 2: 1 green ball and two red or white balls

^{9}C_{2} * ^{3}C_{1} / ^{12}C_{3} Add both cases.

QUESTION: 18

A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?

Solution:

This will be = 1- prob.(both are same in color)

Prob. of both same in color = [^{3}C_{2} + ^{4}C_{2} + ^{3}C_{2}]/ ^{10}C_{2} = 12/45

So required prob. = 1 – 12/45

QUESTION: 19

There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?

Solution:

When both black, prob. = 4/10 * 3/9

When both white, prob. = 6/10 * 5/9 Add both cases.

QUESTION: 20

A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?

Solution:

Case 1: both red

^{5}C_{2} / ^{9}C_{2}

Case 2: both green

^{4}C_{2} / ^{9}C_{2}

Add both cases

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