CBSE Past Question Paper for Class 10 Maths
2018 Section B | Question 12

Probability of selecting a number based on divisiblity. An easy 2 mark question that appeared in 2018 CBSE class 10 maths board paper. Tests your understanding of when a probability of an event can be computed as (1 - probability of another event).

Question 12: An integer is chosen at random between 1 and 100. Find the probability that it is:
(i)   divisible by 8
(ii) not divisible by 8

Video Explanation

Explanatory Answer

Step 1: Find the denominator. Compute the total number of selecting an integer between 1 and 100

Number of ways of choosing an integer at random between 1 and 100 = 98
Note 1 and 100 should not be included.

Part (i) Step 2: Find the numerator. Count numbers between 1 and 100 that are divisible by 8

List of numbers between 1 and 100 that are divisible by 8:
8, 16, 32, 40, 48, 56, 64, 72, 80, 88, 96 = 12 numbers

Part (i) Step 3: Find the probability of the event

Probability of number divisible by 8 = \\frac{\text{Number of integers between 1 and 100 divisible by 8}}{\text{Total number of integers between 1 and 100}})
Probability = \\frac{12}{98}) = \\frac{6}{49})

Part (ii) Step 2: Find the probability that an integer selected at random between 1 and 100 is NOT divisible by 8

Because the set of numbers between 1 and 100 that are divisible by 8 and the set of numbers between 1 and 100 that are not divisible by 8 are
(a) mutually exclusive and
(b) collectively exhaustive,
Probability that the integer is not divisible by 8 = 1 - probability that the number is divisible by 8
1 - \\frac{6}{49}) = \\frac{43}{49})

Note: To be able to use the (1 - probability) method, the two events should be mutually exclusive and collectively exhaustive.