Question

Tickets numbered 2, 3, 4, 5, …, 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is (i) an even number (ii) a number less than 16 (iii) a number which is a perfect square (iv) a prime number less than 40 Select the correct answer from above options

Answer 1

Tickets numbered 2, 3, 4, 5, …, 100, 101 Total number of tickets = 100 (i) Even numbers from 2 to 101 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100 Total number of even number = 50 P(getting a even number) = 50/100 = 1/2. (ii) Numbers less than 16 from 2 to 101 = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 Total number of numbers less than 16 = 14 P(getting a number less than 16) = 14/100 = 7/50. (iii) Perfect square from 2 to 101 = 4, 9, 16, 25, 36, 49, 64, 81, 100 Total number of perfect squares = 9 P(getting a perfect square) = 9/100. (iv) Prime numbers less than 40 from 2 to 101 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 Total number of prime numbers = 12 P(getting a prime number less 40) = 12/100 = 3/25.