Probability Questions and Answers – Set 2

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

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) P2 – 1

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

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

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

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

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

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

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

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

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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