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. Select the correct answer from above options

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