Probability - 3 || Quantitative Aptitude || CAT 2021 || 16 June for CAT & MBA Exams

Question 1

In the MBA Programme of a B - School, there are two sections A and B. 1/4^th of the students in Section A and 4/9^th of the students in section B are girls. If two students are chosen at random, one each from section A and Section B as class representative, the probability that exactly one of the students chosen is a girl, is:

Question 2

If 2 dice are thrown simultaneously, what is the probability that 1 of them shows up ‘2’ and the other shows ‘5’?

Question 3

Direction:
A number is chosen at random from the 30 numbers {10, 11, … 38, 39}. It is known that the numbers with the same first digit have an equal chance of being chosen. Also, a number with 2 as the first digit is twice as likely to be chosen as one with 1 as the first digit, and a number with 3 as the first digit is three times as likely to be chosen as one with 2 as the first digit.

The probability that a number with 2 as its first digit is selected is

Question 4

Direction:
A number is chosen at random from the 30 numbers {10, 11, … 38, 39}. It is known that the numbers with the same first digit have an equal chance of being chosen. Also, a number with 2 as the first digit is twice as likely to be chosen as one with 1 as the first digit, and a number with 3 as the first digit is three times as likely to be chosen as one with 2 as the first digit.

The probability that an even number is selected is

Question 5

Direction:
A number is chosen at random from the 30 numbers {10, 11, … 38, 39}. It is known that the numbers with the same first digit have an equal chance of being chosen. Also, a number with 2 as the first digit is twice as likely to be chosen as one with 1 as the first digit, and a number with 3 as the first digit is three times as likely to be chosen as one with 2 as the first digit.

The probability that a number divisible by 3 is selected is

Question 6

A box contains 5 green, 3 black, and 7 red balls. Two balls are selected at random without replacement from the box. What is the probability that both balls are red?

Question 7

If P(A|B) = 1/3, P(B) = 1/4 and P(A) = 1/2, the probability that exactly one of these events A and B occurs is:

Question 8

What is the probability of rolling three six-sided dice, and getting a different number on each die?

Question 9

In a factory where toys are manufactured, machines A, B and C produce 25%, 35% and 40% of the total toys, respectively. Of their output, 5%, 4% and 2% respectively, are defective toys. If a toy drawn at random is found to be defective, what is the probability that it is manufactured on machine B?

Question 10

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is: