Question

A box contains 20 balls bearing numbers 1, 2, 3, 4, ..., 20. A ball is drawn at random from the box. What is the probability that the number on the ball is divisible by 2 or 3?

Answer 1

Given: A box contains balls numbered 1, 2, ..., 20 and one ball is drawn at random.

Step-wise calculation:

1. Total number of outcomes = 20.

2. Let A = Numbers divisible by 2.

Count |A| = Floor `20/2`

= 10 (2, 4, 6, 8, 10, 12, 14, 16, 18, 20)

3. Let B = Numbers divisible by 3.

Count |B| = Floor `20/3`

= 6 (3, 6, 9, 12, 15, 18)

4. A ∩ B = numbers divisible by 1 cm (2, 3) = 6.

Count |A ∩ B| = Floor `20/6`

= 3 (6, 12, 18)

5. By inclusion–exclusion

Number of favourable outcomes 

= |A| + |B| – |A ∩ B|

= 10 + 6 – 3

= 13

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

= `13/20`

= 0.65

= 65%

The probability that the number on the drawn ball is divisible by 2 or 3 is `13/20` (0.65 or 65%).