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

Correct Answer - ` (i) 1/2 (ii) 7/50 (iii) 9/100 (iv) 3/25` The tickets bear the numbers 2,3,4,…100,101. So, the number of tickets = 100. (i) Out of the given numbers,the even numbers are 2,4,6,8,…100. Their number is 50. ` :. ` P(getting an even number) =` 50/100 = 1/2`. (ii) Out of the given numbers, the numbers of numbers less than 16 is 14. ` :. ` P(getting number less than 16) ` = 14/100 = 7/50`. (iii) Out of the given numbers, the perfect square numbers are ` 2^(2), 3^(2), 4^(2),...,10^(2)`. Their number is 9. ` :. ` P(getting a perfect square number) ` = 9/100`. (iv) Prime numbers less than 40 are 2,3,5,7,11,13,17,19,23,29,31,37. Their numbers is 12. ` :. ` P(getting a prime numbers less than 40) = `12/100 = 3/25`.