Question

A box contains 30 cards, numbered from 1 to 30. A card is drawn from the box at random. Find the probability that the number on the drawn card is prime.

Answer 1

Given: A box contains 30 cards numbered 1 to 30; one card is drawn at random.

Step-wise calculation:

1. List the prime numbers between 1 and 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

2. Number of favourable outcomes = 10.

3. Total number of possible outcomes = 30.

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

= `10/30`

= `1/3`

= 0.3333

The probability that the drawn card shows a prime number is `1/3`.