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

The probability that A get r heads in the three tosses of a coin is
`P(X=r)=.^(3)C_(r)((1)/(2))^(3)`. The probability that A and B both get r heads in three tosses of a coin is
`.^(3)C_(r)((1)/(2))^(3).^(3)C_(r)((1)/(2))^(3)=(.^(3)C_(r))^(2)((1)/(2))^(6)`
`therefore`Required probability
`=underset(r=0)overset(3)(sum)(.^(3)C_(r))^(2)((1)/(2))^(6)`
`=((1)/(2))^(6)(1+9+9+1)=(20)/(64)=(5)/(16)`