A die is relled twice. Find the probability that 5 will come up both the times.

Options

A. `5/6`
B. `1/16`
C. `1/36`
D. `1/6`

Answer

C

Explanation

Number of all possible outcomes = 36.
(i) All those cases where 5 comes up on at least one face are
(1,5),(2,5),(3,5),(4,5),(5,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6).
Number of such cases = 11.
Number of those cases where 5 will not come up any time = 36-11 = 25.
` :. ` P(that 5 will not come up either time) = ` 25/36`.
(ii) All those case where 5 comes up exactly one time are
(1,5),(2,5),(3,5),(4,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6).
Number of such cases = 10.
`:. ` P(that 5 will come up exactly one time) =` 10/36 = 5/18`.
(iii) There is only one case, namely (5,5) when 5 comes up both the times.
` :. ` P(that 5 will come up both the times) ` = 1/36`.