5. A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box. What is the probability that number on the card is
(i) a prime number
(ii) perfect square
(iii) multiple of 5
Sol. The sample space for box containing 20 cards
∴ S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }
∴ n (S) = 20
(i) Let A be the event that number on the card is prime
A = { 2, 3, 5, 7, 11, 13, 17, 19 }
n (A) = 8
P (A) = n (A)/n (S)
∴ P (A) = 8/20
∴ P (A) = 2/5
(ii) Let B be the event that number on the card is a perfect square
B = { 1, 4, 9, 16 }
n (B) = 4
P (B) = n (B)/n (S)
∴ P (B) = 4/20
∴ P (B) = 1/5
(iii)Let C be the event that number on the card is multiple of 5
C = { 5, 10 15, 20 }
n (C) = 4
P (C) = n (C)/n (S)
∴ P (C) = 4/20
∴ P (C) = 1/5
