Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.

Options

A. `2//9`
B. `1//9`
C. `(5)/(18)`
D. None of these

Answer

A

Explanation

Total number of outcomes in sample space, i.e. `n(S)=6xx6=36`
Let E be the event of getting the product perfect square.
`therefore E = {(1,1),(2,2),(4,1),(1,4),(3,3),(4,4),(5,5),(6,6)}`
`therefore n(E )=8`
Hence, the required probability `=(n(E ))/(n(S))=(8)/(36)=(2)/(9)`