Question

A box contains 19 balls bearing numbers 1, 2, 3, ..., 19. A ball is drawn at random from the box. What is the probability that the number of the ball is neither divisible by 5 nor by 10?

Answer 1

Given: A box contains balls numbered 1 through 19; one ball is drawn at random. Find P(the number is neither divisible by 5 nor by 10).

Step-wise calculation:

1. Total number of equally likely outcomes = 19.

2. Numbers between 1 and 19 divisible by 5 are 5, 10, 15 → count = 3.   ...(Numbers divisible by 10 are included among these.)

3. Number of favourable outcomes (neither divisible by 5 nor by 10)

= 19 – 3

= 16

4. Probability = `"Favourable"/"Total"`

= `16/19`

The required probability is `16/19`.