Question : 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
Answer : option (C)
Solution :
The required probability is,
\begin{aligned}\left[ 4C_{0}\left( \dfrac{1}{2}\right) ^{0}\left( \dfrac{1}{2}\right) ^{4}\right] ^{2}+\left[ 4C_{1}\left( \dfrac{1}{2}\right) ^{1}\left( \dfrac{1}{2}\right) ^{3}\right] ^{2}+\ \left[ 4C_{2}\left( \dfrac{1}{2}\right) ^{2}\left( \dfrac{1}{2}\right) ^{2}\right] ^{2}+\left[ 4C_{3}\left( \dfrac{1}{2}\right) ^{3}\left( \dfrac{1}{2}\right) ^{1}\right] ^{2}+\ \left[ 4C_{4}\left( \dfrac{1}{2}\right) ^{4}\left( \dfrac{1}{2}\right) ^{0}\right] ^{2}\end{aligned}=35/128