Probability - MCQ 3

# Probability - MCQ 3

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## 20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations | Probability - MCQ 3

Probability - MCQ 3 for Quant 2022 is part of Quantitative Aptitude for Competitive Examinations preparation. The Probability - MCQ 3 questions and answers have been prepared according to the Quant exam syllabus.The Probability - MCQ 3 MCQs are made for Quant 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Probability - MCQ 3 below.
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Probability - MCQ 3 - Question 1

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

Probability - MCQ 3 - 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.

Detailed Solution for Probability - MCQ 3 - Question 2

Probability = probability of selecting the bag and probability of selecting red ball
(1/2)*(3/11) + (1/2)*(5/12) = 91/264

Probability - MCQ 3 - Question 3

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

Detailed Solution for Probability - MCQ 3 - Question 3

total probability = (12-1)! = 11!
Desired probability = (10 – 1)! = 9!
So, p = (9! *3!) /11! = 3/55

Probability - MCQ 3 - 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.

Detailed Solution for Probability - MCQ 3 - Question 4

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

Probability - MCQ 3 - 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.

Detailed Solution for Probability - MCQ 3 - Question 5

sol⇒ BYBY + YBYB = (5/13)*(8/12)*(4/11)*(7/10) + (8/13)*(5/12)*(7/11)*(4/10)
= 56/429

Probability - MCQ 3 - 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

Detailed Solution for Probability - MCQ 3 - Question 6

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

Probability - MCQ 3 - 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

Detailed Solution for Probability - MCQ 3 - Question 7

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

Probability - MCQ 3 - 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

Detailed Solution for Probability - MCQ 3 - Question 8

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

Probability - MCQ 3 - Question 9

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

Detailed Solution for Probability - MCQ 3 - Question 9

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

Probability - MCQ 3 - 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.

Detailed Solution for Probability - MCQ 3 - Question 10

5c1/15c1 = 1/3

Probability - MCQ 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?

Detailed Solution for Probability - MCQ 3 - Question 11

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
8C2 * 16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 12

Total balls = 15
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = 11C2 / 15C2

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 13

Prob. of black card:
26C2 / 52C2 = 25/102
Prob. of heart card:
13C2 / 52C2 = 3/51

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 14

There are total 26 cards black, and 4 jacks in which 2 are black jacks
So case 1: both are black
26C2 / 52C2
case 2: both are jack
4C2 / 52C2
But now 2 black jacks have been added in both cases, so subtracting their prob. :
2C2 / 52C2
So 325/1326 + 6/1326 – 1/1326

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 15

Case 1: Prob. when 2 men, 1 woman and 1 child
3C2 * 4C1 * 2C1 / 9C4 = 4/21
Case 2: Prob. when 1 man, 2 women and 1 child
3C1 * 4C1 * 2C1 / 9C4 = 2/7
Case 3: Prob. when 1 man, 1 woman and 2 children
3C1 * 4C1 * 2C2 / 9C4 = 2/21

Probability - MCQ 3 - 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?

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 17

Case 1: 0 green ball means all three red or white balls
9C3 / 12C3
Case 2: 1 green ball and two red or white balls
9C2 * 3C1 / 12C3 Add both cases.

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 18

This will be = 1- prob.(both are same in color)
Prob. of both same in color = [3C2 + 4C2 + 3C2]/ 10C2 = 12/45
So required prob. = 1 – 12/45

Probability - MCQ 3 - 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?

Detailed Solution for Probability - MCQ 3 - Question 19

When both black, prob. = 4/10 * 3/9
When both white, prob. = 6/10 * 5/9 Add both cases.

Probability - MCQ 3 - Question 20

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

Detailed Solution for Probability - MCQ 3 - Question 20

Case 1: both red
5C2 / 9C2
Case 2: both green
4C2 / 9C2

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## Quantitative Aptitude for Competitive Examinations

33 videos|34 docs|140 tests