Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

<p>Let x be the number of heads obtained by A, and y be the number of heads obtained by B.</p> <p>Note that x and y are binomial variable with parameters n = 3 and p = ${1 \over 2}$</p> <p>$\therefore$ Probability that both A and B obtained the same number of heads is</p> <p>$$ = P(x = 0)\,.\,P(y = 0) + P(x = 1)\,.\,P(y = 1) + P(x = 2)\,.\,P(y = 2) + P(x = 3)\,.\,P(y = 3)$$</p> <p>$$ = {\left[ {{3_{{C_0}}}{{\left( {{1 \over 2}} \right)}^3}} \right]^2} + {\left[ {{3_{{C_1}}}{{\left( {{1 \over 2}} \right)}^3}} \right]^2} + {\left[ {{3_{{C_2}}}{{\left( {{1 \over 2}} \right)}^3}} \right]^2} + {\left[ {{3_{{C_3}}}{{\left( {{1 \over 2}} \right)}^3}} \right]^2}$$</p> <p>$= {\left( {{1 \over 2}} \right)^6}\left[ {1 + 9 + 9 + 1} \right]$</p> <p>$= {{20} \over {64}}$</p> <p>$= {5 \over {16}}$</p>