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

Options

A. `(1)/(12)`
B. `(1)/(16)`
C. `(3)/(16)`
D. `(5)/(16)`

Answer

D

Explanation

(d) The condition for the sum of five coins to be 12
=(3,3,2,2,2)
The probability of getting 2 on tassing a coin, `p=(1)/(2)` and the probability of getting 3 on tassing a coin,
`q=1-p=1-(1)/(2)=(1)/(2)`
`:.` Required probability `=""^(5)C_(3)((1)/(2))^(3)((!)/(2))^(2)=(10)/(2^(5))=(5)/(16)`