Five coins whose faces are marked 2, 3 are thrown. What is the probability of obtaining a total of 12?

Options

A. `1/16`
B. `3/16`
C. `5/16`
D. `7/16`

Answer

C

Explanation

Let E be the event of total of 12.
`E = (2, 2, 2, 3, 3), (2, 2, 3, 3, 2), (2, 3, 3, 2, 2), (3, 3, 2, 2, 2), (3, 2, 3, 2, 2), (3, 2, 2, 3, 2), (3, 2, 2, 2, 3), (2, 3, 2, 3, 2), (2, 3, 2, 2, 3), (2, 2, 3, 2, 3)`
n(E) = 10
Sample sapce contain total possibility `= 2^(5) = 32`
Hence, n(S) = 32
So, `P(E) = (n(E))/(n(S)) = 10/32 = 5/16`