Question

Cards marked with numbers 1, 3, 5, …, 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is

(i) less than 19,

(ii) a prime number less than 20.

Answer 1

Apply general term formula of an AP, to find the total numbers of cards.

Here a (first term) = 1, d (common difference) = 2 and l( last term) = 101

l = a + (n-1)d

101 = 1 + (n-1)(2)

n = 51

Total number of cards = 51

(i)

Favorable outcome = Numbers less than 19 = 1, 3, 5, 7, 9, 11, 13, 15, 17

Favorable number of outcomes = 9

P(getting a card number less than 19) = 9/51

(ii) Favorable outcome = a prime number less than 20 = 3, 5, 7, 11, 13, 15, 17, 19

Favorable number of outcomes = 7

P(getting a card with a prime number less than 20) = 7/51