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 card drawn is
(a) divisible by 5
(b) a perfect square

Answer 1

Total numbers of cards = 60 - 13 + 1 = 48
(a) Cards with numbers divisible by 5 are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Number of such cards = 10
∴ P(getting a number divisible by 5) = $\frac{10}{48}=\frac{5}{24}$

(b) Perfect squares are 16, 25, 36, 49.
Number of such cards = 4
∴ P(getting a perfect square) = $\frac{4}{48}=\frac{1}{12}$