A Son Born on a Tuesday

Your new coworker mentions she has exactly two children and, in passing, that at least one of them is a boy who was born on a Tuesday. Model each child independently as boy or girl with probability 12 \frac{1}{2} , with birth weekday uniform over the 7 days and independent of everything else. Given exactly this information, what is the probability that both of her children are boys?

Answer

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