A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

(a)  1/25

(b) 24/25

(c) 2/25

(d) 1/3

Sol:

The total number of ways of choosing number from 1 to 25 by both the players = 25 25

=625. There are 25 ways in which number chosen by both the players is same.

The probability that they will prize in a single trial =25/625=1/25

Required, Probability that they will not win a prize in a single trial =1-1/25=24/25