Question

A box contains 25 cards numbered from 1 to 25. A card is drawn from the box at random. Find the probability that the number on the drawn card is
(i) even
(ii) prime
(iii) multiple of 6

Answer 1

The possible outcomes are 1,2, 3,4, 5................25.
Number of all possible outcomes = 25

(i) Out of the given numbers, the even numbers are 2, 4, 6, 8,10,12,14,16, 18, 20,22 and 24. Let E₁ be the event of getting an even number.
Then, number of favourable outcomes = 12​
∴ P (getting an even number) = $\frac{12}{25}$

(ii) Out of the given numbers, the prime numbers are 2, 3, 5, 7,11,13, 17, 19 and 23. Let E₂ be the event of getting a prime number.
Then,​ number of favourable outcomes =​ 9
∴ P (getting a prime number) = $\frac{9}{25}$

(iii) Out of the given numbers, the numbers that are multiples of 6 are 6,12,18 and 24.
Let E₃ be the event of getting a multiple of 6.

Then,​ number of favourable outcomes = 4
∴ P (getting a multiple of 6) = $\frac{4}{25}$