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 ,

Options

A. `1//25`
B. `24//25`
C. `2//25`
D. none of these

Answer

B

Explanation

The number of ways in which either player can choose a number from 1 to 25 is 25, so the total number of ways of choosing numbers is `25xx25=625`. There are 25 ways in which the numbers chosen by both players is the same. Therefore, the probability they will win a prize in a single trial is `(25)/(625)=(1)/(25)`.
Hence, the probability that the will not win a prize in a single trial `=1-(1)/(25)=(24)/(25)`.