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 divisible by 3 or 5?

Answer 1

Given: A box contains balls numbered 1, 2, ..., 19 and one ball is drawn at random; find the probability the number is divisible by 3 or 5.

Step-wise calculation:

1. Total possible outcomes = 19.

2. Multiples of 3 in {1,...,19}: 3, 6, 9, 12, 15, 18 → count = 6.

3. Multiples of 5 in {1,...,19}: 5, 10, 15 → count = 3.

4. Overlap (multiples of both 3 and 5) = multiples of 15: {15} → count = 1.

5. By inclusion–exclusion

Favourable outcomes

= 6 + 3 – 1 

= 8

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

= `8/19`

The probability that the drawn number is divisible by 3 or 5 is `8/19`.