**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