Question

A pair of fair dice is tossed. Find the probability that the maximum of the two numbers is greater than $4$.

• A. $\frac{5}{9}$
• B. $\frac{4}{9}$
• C. $\frac{2}{9}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{9}$

Given, Two fair dice have been rolled
No. of selections such that maximum of two dice should be greater than $4$.

$=(1,5).(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4)(5,5),(5,6)$

$,(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)=20$ cases
Total no.of cases when two dice roles $=6\times 6=36$
Required probability $=\frac{20}{36}=\frac{5}{9}$