Gary has $2$ children. We know one is a boy born on a Friday. Assume birthing boys and girls are equally likely, being born on any day of the week is equally likely, and that these properties are independent of each other, as well as independent from child to child. The probability that both of Gary's children are boys is $\frac{a}{b}$ where $a$ and $b$ are relatively prime integers. Find $a + b.$

Let's think step by step and output the final answer within \boxed{}.
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