Explanation

(a)
A leap year consists of 366 days $ie$, 52 full weeks and two extra days. These two extra days can be any one of the following possible outcomes; (i) Monday and Tuesday, (ii) Tuesday and Wednesday, (iii) Wednesday and Thursday, (iv) Thursday and Friday, (v) Friday and Saturday, (vi) Saturday and Sunday, (vii) Sunday and Monday.
Let $A\ and\ B$ be the events that a leap year contains 53 Thursdays and 53 Fridays respectively. Then,
$P(A) = \frac{2}{7},P(B) = \frac{2}{7}\ and\ P(A \cap B) = \frac{1}{7}$
$\therefore$ Required probability is given by
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= \frac{2}{7} + \frac{2}{7} - \frac{1}{7} = \frac{3}{7}$