Question

Cards marked with numbers 13, 14, 15, ..., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the drawn card is (i) divisible by 5 (ii) a perfect square.

Answer 1

The possible outcomes are 13,14, 15, 16................60.
Number of all possible outcomes = 48

(i) Out of the given numbers, the numbers divisible by 5 are 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60.
Let E₁ be the event of getting a number divisible by 5.
Then, number of favourable outcomes = 10​
∴ P (getting a number divisible by 5) = $\frac{10}{48}=\frac{5}{24}$

(ii) Out of the given numbers, the perfect squares are 16, 25, 36, and 49.
Let E₂ be the event of getting a perfect square.
Then, number of favourable outcomes = 4​
∴ P (getting a perfect square) = $\frac{4}{48}=\frac{1}{12}$