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Test Level 1: Probability - 1 - CAT MCQ


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

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

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the drawn ticket contains a number, which is a multiple of 3 or 7?

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

Favourable cases = 3, 6, 9, 12, 15, 18, 7, 14
Probability = 8/20 = 2/5

Test Level 1: Probability - 1 - Question 2

A husband and a wife appear in an interview for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that none of them will be selected?

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

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Test Level 1: Probability - 1 - Question 3

A piece of work is given to 6 men and their probabilities for doing the work are 1/7, 1/4, 1/6, 1/8, 1/5 and 1/3. Find the probability that the work is done.

Detailed Solution for Test Level 1: Probability - 1 - Question 3

Probability that the work is done

Test Level 1: Probability - 1 - Question 4

Two cards are drawn from a pack of 52 cards. The probability that one of the cards drawn is an ace and the other is a spade but none of the cards drawn is an ace of spades is

Detailed Solution for Test Level 1: Probability - 1 - Question 4

Number of Ace except ace of spade = 4 - 1 = 3
Number of spade except ace of spade = 13 - 1 = 12

Test Level 1: Probability - 1 - Question 5

Two dice are rolled. What is the probability that the total score is not a prime number?  

Detailed Solution for Test Level 1: Probability - 1 - Question 5

S = sample space.
n(S) = 36.
E = event of getting a prime number = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)}.
n(E) = 15.
P(not a prime number) = (1 - (15/36)) = 21/36 = 7/12.

Test Level 1: Probability - 1 - Question 6

A die is rolled thrice. Find the probability of getting a number less than 5 in each case.

Detailed Solution for Test Level 1: Probability - 1 - Question 6

Total cases = 63
Favorable cases = 43
Probability of getting a number less than 5 in each case

Test Level 1: Probability - 1 - Question 7

A purse contains two 50 paisa coins, four 25 paisa coins and six 10 paisa coins. If 5 coins are taken out from the purse at random, what is the probability that the sum taken out is at least Rs. 1.50?

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

5 coins can be selected at random as 2 + 4 + 6 = 12 coins in C(12, 5) ways.
They will amount to at least Rs. 1.50 if two 50 paisa and three 25 paisa coins are selected or one 50 paisa and four 25 paisa coins are selected or two 50 paisa coins, two 25 paisa coins and one 10 paisa coin are selected.
This can be done in 2C2 × 4C3 + 2C1 × 4C4 + 2C2 × 4C2 × 6C1 = (4 + 2 + 36) = 42 ways.
Thus, required probability is

Test Level 1: Probability - 1 - Question 8

If a card is drawn at random from 100 cards numbered 1 to 100, find the probability that the number on the card drawn is a perfect square.

Detailed Solution for Test Level 1: Probability - 1 - Question 8

Favourable cases = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Number of favourable cases = 10
Required probability = 10/100 = 1/10

Test Level 1: Probability - 1 - Question 9

Two persons throw a pair of dice alternately till, one gets a total of 9 and wins the game. If A takes the first throw, then the probability that A wins the game is

Detailed Solution for Test Level 1: Probability - 1 - Question 9

P(win) = 4/36 = 1/9
P(loss) = 8/9

Test Level 1: Probability - 1 - Question 10

A coin is tossed (m + n) times (m > n). The probability of getting at least m consecutive heads is

Detailed Solution for Test Level 1: Probability - 1 - Question 10

Let the value of m = 2 and n = 1
Total outcomes will be 8, and probability of getting two consecutive outcomes will be
HHT, HHH and THH, i.e.3/8, only option 3 satisfies for m = 2 and n = 1

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