This set of Aptitude Questions and Answers (MCQs) focuses on “Probability – Set 2”.

1. What is the probability that a number selected at random from 1 to 15 is a multiple of 3?

a) 2 / 5

b) 3 / 5

c) 1 / 3

d) 2 / 3

View Answer

Explanation:

Total possible outcomes = 15

Favorable outcomes = 3, 6, 9, 12, 15

Probability = 5 / 15 = 1 / 3

2. If the probability of an event is Q, then what will be the probability of its complementary event?

a) 1 – P

b) P – 1

c) 1 – 1 / P

d) P^{2} – 1

View Answer

Explanation: Given,

Probability = P

Probability of complementary of P = 1 – P.

3. What is the probability of having 53 Tuesdays in a non – leap year?

a) 5 / 7

b) 1 / 7

c) 2 / 7

d) 3 / 7

View Answer

Explanation:

A non – Leap year has 365 days which is 52 weeks and1 extra day.

For this one day

Total possible outcomes = 7 (from Sunday to Saturday)

Favorable outcomes = 1 (Tuesday)

Probability = 1 / 7

4. Hundred balls are numbered from 1 to 100. What is the probability of getting a ball having a prime number?

a) 1 / 4

b) 3 / 4

c) 2 / 3

d) 1 / 5

View Answer

Explanation:

Total possible outcomes = 100

Favorable outcomes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97) = 25

Thus, probability = 25 / 100

= 1 / 4

5. A bag contains 10 red cards and some yellow cards. If the probability of getting yellow cards is thrice the probability of getting a red card, then what is the number of yellow cards?

a) 25

b) 20

c) 30

d) 15

View Answer

Explanation: Given,

Red cards = 10

Let the yellow cards be x. Then total number of cards = 10 + x.

According to the question

x / (10 + x) = 3 * 10 / (10 + x)

➩ x = 30

6. A box contains 1000 pens of which 25 are defective. What is the probability of drawing a defective pen from the box?

a) 1 / 8

b) 1 / 12

c) 1 / 4

d) 1 / 40

View Answer

Explanation:

Total possible outcomes = 1000

Favorable outcomes = 25

Probability = 25 / 1000 = 1 / 40

7. Cards marked with numbers 1 to 100 are placed in a box. One card is drawn from this box randomly, then what is the probability that the number on the card is a perfect square?

a) 1 / 10

b) 1 / 20

c) 1 / 15

d) 1 / 5

View Answer

Explanation:

Total possible outcomes = 100

Favorable outcomes = (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) = 10

Probability = 10 / 100 = 1 / 10

8. A number is selected at random from the first fifty natural numbers. What is the probability that the number is divisible by 2, 3 and 4?

a) 4 / 25

b) 1 / 25

c) 2 / 25

d) 3 / 25

View Answer

Explanation:

Total possible outcomes = 50

Favorable outcomes = 12, 24, 36, 48 = 4

Probability = 4 / 50 = 2 / 25

9. A jar has 48 marbles of which few are black and others are red. If the probability of getting a black marble is \(\frac {3}{4}\), then what will be the number of red marbles?

a) 10

b) 12

c) 14

d) 15

View Answer

Explanation: Let the number of red marbles be z.

P(red) = 1 – P(black)

➩ z / 48 = 1 – \(\frac {3}{4}\)

➩ z / 48 = \(\frac {1}{4}\)

➩ z = 48 / 4

➩ z = 12

10. What is the probability of getting 53 Wednesdays in a leap year?

a) 2 / 7

b) 1 / 7

c) 3 / 7

d) 4 / 7

View Answer

Explanation: Leap year has 52 weeks and two days i.e., 52 Wednesdays are there and two days are left.

Those two days can be = (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)

There are two pairs having Wednesday.

Thus, Probability (53 Wednesday) = 2 / 7.

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