Question

15 cards, numbered 1, 2, 3...., 15 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an even number (ii) a number divisible by 2 or 3.

Answer 1

Given:15 cards numbered 1, 2,...,15 are equally likely; one card is drawn at random.

Step-wise calculation:

1. Total number of outcomes = 15.

2. (i) Even numbers in 1..15: 2, 4, 6, 8, 10, 12, 14 → 7 favourable.

Probability = `"Favourable"/"Total"`

= `7/15`

3. (ii) Numbers divisible by 2 or 3:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14 (7)

Multiples of 3: 3, 6, 9, 12, 15 (5)

Multiples of both 2 and 3 i.e., 6: 6, 12 (2) 

Using inclusion–exclusion:

Favourable = 7 + 5 – 2

= 10 

Probability = `10/15`

= `2/3`

(i) Probability the card shows an even number = `7/15`. 

(ii) Probability the card shows a number divisible by 2 or 3 = `2/3`.