Two players toss `4` coins each. The probability that they both obtain the same number of heads is a. `5//256` b. `1//16` c. `35//128` d. none of these

Options

A. `5//256`
B. `1//16`
C. `35//128`
D. None of these

Answer

C

Explanation

The required probability is
`=[""^(4)C_(0)((1)/(2))^(0)((1)/(2))^(4)]^(2)+[""^(4)C_(1)((1)/(2))^(1)((1)/(2))^(3)]^(2)`
`=[""^(4)C_(2)((1)/(2))^(2)((1)/(2))^(2)]^(2)+[""^(4)C_(3)((1)/(2))^(3)((1)/(2))^(1)]^(2)`
`+[""^(4)C_(4)((1)/(2))^(4)((1)/(2))^(0)]^(2)=35/128`