Question

A bag contains 13 red cards, 13 black cards and 13 green cards. Each set of cards are numbered 1 to 13. From these cards, a card is drawn at random. What is the probability that the card drawn is a:

1. green card?
2. a card with an even number?
3. a red or black card with a number which is a multiple of three?

Answer 1

Given: The bag has 13 red, 13 black and 13 green cards, numbered 1 to 13 in each colour. Total cards = 13 + 13 + 13 = 39.

Step-wise calculation:

a. Green card:

Favourable outcomes = 13 all green cards.

Probability = `13/39 = 1/3 ≈ 0.3333`.

b. Card with an even number:

Even numbers between 1 and 13: 2, 4, 6, 8, 10, 12 → 6 per colour.

Total favourable = 6 × 3 = 18.

Probability = `18/39 = 6/13 ≈ 0.4615`.

c. A red or black card whose number is a multiple of 3:

Multiples of 3 in 1..13: 3, 6, 9, 12 → 4 numbers per colour.

Colours allowed: red or black → 2 colours → favourable = 4 × 2 = 8.

Probability = `8/39 ≈ 0.2051`.