Mrs. Grundy's Conditional Probability Problem Mrs. Grundy has two children. Given that Mrs. Grundy has at least one child born on a Monday, what is the probability that both her children were born on Mondays? Assume that each child was equally likely to be born on any day of the week, and that the two birthdays are independent (Mrs. Grundy doesn't have twins!). I ended up with 4/25 but I was wrong. Thanks!

Observe that: \begin{align*} \Pr[\text{both Monday} \mid \text{at least one Monday}] &= \frac{\Pr[\text{both Monday and at least one Monday}]}{\Pr[\text{at least one Monday}]} \\\ &= \frac{\Pr[\text{both Monday}]}{1 - \Pr[\text{both not Monday}]} \\\ &= \frac{(\frac{1}{7})^2}{1 - (\frac{6}{7})^2} \\\ &= \frac{1}{49 - 36} \\\ &= \frac{1}{13} \end{align*}