Explanation

(c)
The probability that $A$ get $r$ heads in the three tosses of a coin is
$P(X = r) = {\ ^{3}C}_{r}\left( \frac{1}{2} \right)^{3}$. The probability that $A$ and $B$ both get $r$ heads in three tosses of a coin is
$\ ^{3}C_{r}\left( \frac{1}{2} \right)^{3}.{\ ^{3}C}_{r}\left( \frac{1}{2} \right)^{3}$
$= (^{3}C_{r}\left. \ \ \right)^{2}\left( \frac{1}{2} \right)^{6}$
$\therefore$ Required probability $= \sum_{r = 0}^{3}{(^{3}C_{r}\left. \ \ \right)^{2}\left( \frac{1}{2} \right)^{6}}$
$= \left( \frac{1}{2} \right)^{6}(1 + 9 + 9 + 1) = \frac{20}{64} = \frac{5}{16}$