Question

A box contains 30 cards, numbered 1 to 30. A card is drawn from the box at random. Find the probability that the number of the drawn card is (i) even, (ii) prime and (iii) multiple of 7.

Answer 1

The possible outcomes are 1, 2, 3, 4, 5,...................30.

Number of all possible outcomes = 30

(i) Out of the given numbers, the even numbers are :

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

Let E₁ be the event of getting an even number.
Then, number of favourable outcomes = 15​
∴ P (getting an even number) = $\frac{15}{30}=\frac{1}{2}$

(ii) Out of the given numbers, the prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Let E₂ be the event of getting a prime number.
Then, number of favourable outcomes = 10​
∴ P (getting a prime number) = $\frac{10}{30}=\frac{1}{3}$

(iii) Out of the given numbers, the multiples of 7 are:
7, 14, 21 and 28
Let E₃ be the event of getting a multiple of 7.
Then, number of favourable outcomes = 4​
∴ P (getting a multiple of 7) = $\frac{4}{30}=\frac{2}{15}$