Mrs. Grundy has two children. Given that Mrs. Grundy's older child was 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.
The obvious answer would be $\frac{1}{7}$ since the second child is equal likely to be born on any day of the week. But I got this problem out of a high-level math book and that would be too easy. Is $\frac{1}{7}$ the answer? Or am I missing something really big here?
UPDATE: $\frac{1}{7}$ was the answer and I was correct. And no, this is not a duplicate. The other problem has a different part, so whoever marked this question a duplicate was not careful enough to read the whole question.
Best Answer
The obvious answer is the right one.
To see this formally, let $Y$ be the event that the younger child was born on Monday. Let $O$ be the event that the older child was born on Monday. We are interested in the probability of $Y \cap O$, that both children were born on Monday, given $O$. Using the definition of conditional probability and independence we have
$$P(Y \cap O \mid O) = \frac{P(Y \cap O)}{P(O)} = \frac{P(Y)P(O)}{P(O)} = P(Y) = 1/7$$