If `Aa n dB` each toss three coins. The probability that both get the same number of heads is `1//9` b. `3//16` c. `5//16` d. `3//8`

Options

A. `(1)/(9)`
B. `(3)/(16)`
C. `(5)/(16)`
D. `(3)/(8)`

Answer

C

Explanation

(c ) The probability that A get get r heads in the three tossed of a coin is `P(X=r)=""^(3)C_(r )((1)/(2))^(3)`. The probability that A and B both getr heads in three tosses of a coin is
`""^(3)C_(r )((!)/(2))^(3).""^(3)C_(r )((1)/(2))^(3)=(""^(3)C_(r ))^(2)((1)/(2))^(6)`
[`:'` A and B are independent events]
`:.` Required probability
`=underset(r=0)overset(3)Sigma(""^(3)C_(r ))^(2)((1)/(2))^(6)=((1)/(2))^(6)[(""^(3)C_(0))^(2)+(""^(3)C_(1))^(2)+(""^(3)C_(1))^(2)+(""^(3)C_(3))^(2)]`
`=((1)/(2))^(6)(1+9+9+1)=(20)/(64)=(5)/(16)`