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 proablitty that A gets r heads in three tosses of a coin is
`P(X=r)=""^(3)C_(r)((1)/(2))^(r)((1)/(2))^(3-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)`
Hence, the required probability is
`underset(r=0)overset(3)sum(""^(3)C_(r))((1)/(2))^(6)=((1)/(2))^(6){1+9+9+1}=(20)/(64)=5/16`