Probability (Medium Level) - CAT MCQ

# Probability (Medium Level) - CAT MCQ

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## 11 Questions MCQ Test Quantitative Aptitude (Quant) - Probability (Medium Level)

Probability (Medium Level) for CAT 2024 is part of Quantitative Aptitude (Quant) preparation. The Probability (Medium Level) questions and answers have been prepared according to the CAT exam syllabus.The Probability (Medium Level) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Probability (Medium Level) below.
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Probability (Medium Level) - Question 1

### Two fair dices are thrown. Given that the sum of the dice is less than or equal to 4, find the probability that only one dice shows two.

Detailed Solution for Probability (Medium Level) - Question 1

The possible outcomes are:
(1, 1); (1, 2); (2, 1), (2, 2); (3, 1); (1, 3).
Out of six cases, in two cases there is exactly one ‘2’
Thus, the correct answer is 2/6 = 1/3.

Probability (Medium Level) - Question 2

### There are two bags, one of them contains 5 red and 7 white balls and the other 3 red and 12 white balls, and a ball is to be drawn from one or the other of the two bags. Find the chance of drawing a red ball.

Detailed Solution for Probability (Medium Level) - Question 2

The event can be defined as:
The first bag is selected and a red ball is drawn.
or a second bag is selected and a red ball is drawn.
1/2 X 5/12 + 1⁄2 X 3/15 = (5/24) + (3/30) = 37/120

Probability (Medium Level) - Question 3

### In two bags there are to be put altogether 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws one ball from either bag the greatest chance of drawing a red ball?

Detailed Solution for Probability (Medium Level) - Question 3

For the greatest chance of drawing a red ball the distribution has to be 1 Red in the first bag and 4 red + 12 white balls in the second bag. This gives us
½ X 1+½ X 4/16 =5 / 8

Probability (Medium Level) - Question 4

What is the chance that a leap year, selected at random, will contain 53 Sundays?

Detailed Solution for Probability (Medium Level) - Question 4

A leap year has 366 days – which means 52 completed weeks and 2 more days. The last two days can be (Sunday, Monday) or (Monday, Tuesday) or ....... (Saturday, Sunday).2 scenarios out of 7 have a 53rd Sunday. Thus, 2/7 is the required answer

Probability (Medium Level) - Question 5

A child is asked to pick up 2 balloons from a box containing 10 blue and 15 red balloons. What is the probability of the child picking, at random, 2 bal- loons of different colours?

Detailed Solution for Probability (Medium Level) - Question 5

Blue and Red or Red and Blue
= (10/25) X (15/24) + (15/25) X(10/24) = (1/2).

Probability (Medium Level) - Question 6

Three fair dice are rolled simultaneously. Find the probability that the first die shows a composite number, second die shows an odd number and third die shows an odd prime number.

Detailed Solution for Probability (Medium Level) - Question 6

Required probability = probability of first die shows a composite number x probability of second die shows an odd number x probability of third die shows an odd prime number
= 2/6 X 3/6 X 2/6 = 1/18.

Probability (Medium Level) - Question 7

Three groups of children contain 3 girls and 1 boy, 2 girls and 2 boys, and 1 girl and 2 boys respectively. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is

Detailed Solution for Probability (Medium Level) - Question 7

Girl and Boy and Boy or Boy and Girl and Boy Or Boy and Boy and Girl
= (3/4) X(2/4) X(2/3) + (1/4) X(2/4) X(2/3) + (1/4) X(2/4) X(1/3) = 18/48 = 3/8.

Probability (Medium Level) - Question 8

Ross draws a card from a pack of 52, replaces it and shuffles it. He continues doing it until he draws a heart. What is the probability that he has to make 3 trials?

Detailed Solution for Probability (Medium Level) - Question 8

The event definition here is that first is not a heart and second is not a heart and third is a heart = (3/4) X(3/4) X (1/4) = 9/64

Probability (Medium Level) - Question 9

For the above question, the probability that exactly 3 tests will be required to identify the 2 faulty machines is,

Detailed Solution for Probability (Medium Level) - Question 9

Faulty and not Faulty and Faulty or Not Faulty and faulty and faulty
= (2/4) X(2/3) X(1/2) + (2/4) X (2/3) X(1/2)
= 1/3

Probability (Medium Level) - Question 10

12 people are seated around a round table. What is the probability that two particular persons sit together ?

Detailed Solution for Probability (Medium Level) - Question 10

P = Total no of ways in which two people sit together / Total No. of way
= (10! X 2!)/11!
= 2/11

Probability (Medium Level) - Question 11

There are 4 red, 6 blue and 8 white balls in a bag. Raju drew 2 balls from it one after another. Find the probability of the second ball drawn being blue if the first ball is replaced.?

Detailed Solution for Probability (Medium Level) - Question 11

The required probability = (Probability of drawing any ball from the bag as the first ball). (Probability of drawing a blue ball from it as the second ball)
= 6/18 = 1/3

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