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Test Level 1: Probability - 2 - CAT MCQ


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20 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Probability - 2

Test Level 1: Probability - 2 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Probability - 2 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Probability - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Probability - 2 below.
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Test Level 1: Probability - 2 - Question 1

What are the odds against drawing 2 red balls from a bag containing 3 red and 2 white balls?  

Detailed Solution for Test Level 1: Probability - 2 - Question 1

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

Test Level 1: Probability - 2 - Question 2

Three unbiased coins are tossed. What is the probability of getting at most two tails?  

Detailed Solution for Test Level 1: Probability - 2 - 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

In a single throw of two dice, find the probability that neither a doublet nor a total of 10 will appear.

Detailed Solution for Test Level 1: Probability - 2 - 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

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 for Test Level 1: Probability - 2 - 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

Three dice are rolled together. What is the probability of getting the same number on the three?

Detailed Solution for Test Level 1: Probability - 2 - 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

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 for Test Level 1: Probability - 2 - 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

Two dice are thrown. Find the probability that the product of two numbers received is even.

Detailed Solution for Test Level 1: Probability - 2 - Question 7


Total cases = 62 
Both odd numbers
 

Test Level 1: Probability - 2 - Question 8

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 for Test Level 1: Probability - 2 - 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

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 for Test Level 1: Probability - 2 - Question 9

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

Test Level 1: Probability - 2 - Question 10

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 for Test Level 1: Probability - 2 - Question 10

P(None is defective)

P(at least one is defective) 

Test Level 1: Probability - 2 - Question 11

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 for Test Level 1: Probability - 2 - Question 11

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

Test Level 1: Probability - 2 - Question 12

What is the probability of getting a sum of 6 from two throws of a dice?

Detailed Solution for Test Level 1: Probability - 2 - 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

A coin is tossed five times. Find the probability of getting 2 heads and 3 tails.

Detailed Solution for Test Level 1: Probability - 2 - 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

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 for Test Level 1: Probability - 2 - Question 14

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

Test Level 1: Probability - 2 - Question 15

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 for Test Level 1: Probability - 2 - 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

The letters of the word 'LEADING' are placed at random in a row. What is the probability that three vowels come together?

Detailed Solution for Test Level 1: Probability - 2 - 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

The probability that in a group of 3 people, at least two will have the same birthday is

Detailed Solution for Test Level 1: Probability - 2 - Question 17

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

Test Level 1: Probability - 2 - Question 18

In throwing a fair dice, what is the probability of getting the number ‘3’?

Detailed Solution for Test Level 1: Probability - 2 - Question 18

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

Test Level 1: Probability - 2 - Question 19

Find the chance of throwing at least one ace in a simple throw with two dice.

Detailed Solution for Test Level 1: Probability - 2 - 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

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 for Test Level 1: Probability - 2 - Question 20

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

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