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CAT Exam  >  CAT Test  >  Level-wise Tests  >  Test Level 1: Probability - 2 - CAT MCQ

Test Level 1: Probability - 2 CAT MCQs & solutions - Free


MCQ Practice Test & Solutions: Test Level 1: Probability - 2 (20 Questions)

You can prepare effectively for CAT Level-wise Tests for CAT with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test Level 1: Probability - 2". These 20 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 40 minutes
  • - Number of Questions: 20

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Test Level 1: Probability - 2 - Question 1
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What are the odds against drawing 2 red balls from a bag containing 3 red and 2 white balls?  

Detailed Solution: Question 1

Probability of selecting two red balls = 
Odds in favour = 3 : 7
Odds against = 7 : 3

Test Level 1: Probability - 2 - Question 2
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Three unbiased coins are tossed. What is the probability of getting at most two tails?  

Detailed Solution: Question 2

S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH }.
E = {HHT, HTH, THH, HTT, THT, TTH, HHH}.
Therefore, P(E) = 7/8

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Test Level 1: Probability - 2 - Question 3
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In a single throw of two dice, find the probability that neither a doublet nor a total of 10 will appear.

Detailed Solution: Question 3

Total outcomes = 36
Favourable outcomes for getting a doublet or a total of 10 = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (4, 6), (6, 4)]
Probability = 8/36
Probability that neither a doublet nor a total of 10 will appear 

Hence, answer option 1 is correct.

Test Level 1: Probability - 2 - Question 4
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The number lock of a suitcase has 4 wheels, each labelled with ten digits, i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the sequence to open the suitcase?

Detailed Solution: Question 4

There are 10C4 × 4! = 5040 sequences of 4 distinct digits, out of which there is only one sequence in which the lock opens.
Required probability = 1/5040

Test Level 1: Probability - 2 - Question 5
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Three dice are rolled together. What is the probability of getting the same number on the three?

Detailed Solution: Question 5

Total number of possible cases = 63 = 216
Favourable number of cases = 6
Probability = 6/216 = 1/36

Test Level 1: Probability - 2 - Question 6
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In a class, there are 15 boys and 10 girls. Three students are selected at random. Find the probability that 1 girl and 2 boys are selected.

Detailed Solution: Question 6

Number of ways of choosing 1 girl out of 10 = 10C1
Number of ways of choosing 2 boys out of 15 = 15C2
Total number of ways of choosing 3 students out of 25 (15 + 10) = 25C3

Test Level 1: Probability - 2 - Question 7
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Two dice are thrown. Find the probability that the product of two numbers received is even.

Detailed Solution: Question 7


Total cases = 62 
Both odd numbers
 

Test Level 1: Probability - 2 - Question 8
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A biased coin is tossed 700 times. Heads appears 300 times and tails appears 400 times. If the coin is tossed again, the probability of getting heads is

Detailed Solution: Question 8


Number of favourable outcomes = 300, as heads has appeared 300 times.
Total number of possible outcomes = 700, as the coin is tossed 700 times.
⇒ Probability = 300/700 = 3/7

Test Level 1: Probability - 2 - Question 9
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The probability that A can solve a problem is 2/3 and the probability that B can solve the problem is 3/4. The probability that at least one of A and B will be able to solve the problem is

Detailed Solution: Question 9

Probability that at least one of A and B will solve the problem

Test Level 1: Probability - 2 - Question 10
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There are 20 pens in a bag. 4 pens are defective. Two pens are chosen at random from the bag. The probability that at least one of these is defective is

Detailed Solution: Question 10

P(None is defective)

P(at least one is defective) 

Test Level 1: Probability - 2 - Question 11
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The chances of winning of two race horses are 1/3 and 1/6. What is the probability that at least one will win, if the horses are running in different races? 

Detailed Solution: Question 11

Probability that at least one horse will win = 1 - Probability that neither horse will win

Test Level 1: Probability - 2 - Question 12
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What is the probability of getting a sum of 6 from two throws of a dice?

Detailed Solution: Question 12

S = Sample space = 36.
E = Event of getting the sum as 6.
Favorable outcomes = {(2,4), (4,2), (1,5), (5,1), (3,3)}.
So, n(E) = 5.
P(E) = 5/36.

Test Level 1: Probability - 2 - Question 13
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A coin is tossed five times. Find the probability of getting 2 heads and 3 tails.

Detailed Solution: Question 13

Total number of cases when a coin is flipped five times = 32
Favourable number of cases (2 heads and 3 tails) = 5C2 or 5C3 = 10
Required probability = 10/32 = 5/16

Test Level 1: Probability - 2 - Question 14
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A bag contains 6 white and 9 black balls. If three balls are drawn at random, then find the probability that all of them are black.

Detailed Solution: Question 14

Total number of outcomes = 15C3
Number of favourable outcomes = 9C3

Test Level 1: Probability - 2 - Question 15
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Two dice are rolled simultaneously. Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die.

Detailed Solution: Question 15

E = {(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (3, 4), (3, 6), (6, 2), (6, 4)}
n(E) = 11
n(s) = 36

Test Level 1: Probability - 2 - Question 16
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The letters of the word 'LEADING' are placed at random in a row. What is the probability that three vowels come together?

Detailed Solution: Question 16

Total number of sample spaces = 7!
Total number of favourable outcomes = 3! × 5!
Required probability = (3! × 5!)/7!
= 1/7

Test Level 1: Probability - 2 - Question 17
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The probability that in a group of 3 people, at least two will have the same birthday is

Detailed Solution: Question 17

Let A be the event that at least two people have the same birthday.
Then,

Test Level 1: Probability - 2 - Question 18
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In throwing a fair dice, what is the probability of getting the number ‘3’?

Detailed Solution: Question 18

Out of a total of 6 occurrences, 3 is one possibility = 1/6.

Test Level 1: Probability - 2 - Question 19
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Find the chance of throwing at least one ace in a simple throw with two dice.

Detailed Solution: Question 19

Event definition is:
(1 and 1) or (1 and 2) or (1 and 3) or (1 and 4) or  
(1 and 5) or (1 and 6) or (2 and 1) or (3 and 1) or
(4 and 1) or (5 and 1) or (6 and 1)
Total 11 out of 36 possibilities = 11/36

Test Level 1: Probability - 2 - Question 20
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From a pack of 52 cards, two are drawn at random. Find the chance that one is a knave and the other a queen.

Detailed Solution: Question 20

Knave and queen or Queen and Knave → 4/52 × 4/51 + 4/52 × 4/51 = 8/663 

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About this CAT Practice Test

This test contains 20 MCQs on Test Level 1: Probability - 2 with detailed solutions for each question. It is part of the Level-wise Tests for CAT course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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