**ANSWER**:

*13/27.*
**EXPLANATION**: At first it seems the answer is 50% (or 33% if you're familiar with the simple
version of the

Two Child Problem).
Most people will be amazed that the "born on a Tuesday" detail has an effect on the probability!

The probability is calculated using Bayes' Theorem or by using a more basic approach consisting of
a table that includes all the possible combinations for the two children based on the details that were
provided. There are 196 combinations possible of gender and day of the week:

The first two characters of each combination refer to the first child and the next to characters refer
to the second child. B and G are used to indicate a boy or girl and the numbers 1 though 7 are used to
indicate the day the child was born on (Monday through Sunday). B1B1 means child 1 is a boy born on the
first day of the week (Monday) and child two is also a boy born on the first day of the week (Monday).

The combinations that include a boy born on a tuesday (B2) are highlighted, there are 27 in all and
these represent the possible combinations for the man's children given his statement. Of the 27
possibilities, 13 consist of two boys. So the probability is 13/27.

Those familiar with the classic Two Child Problem might wonder why the answer changes from 1/3 to 13/27
by adding the detail about the day of the week. By being more specific about one of his children, there
is a smaller chance that he is referring to either one of the children and a greater chance that he is
referring to one in particular. There's less "probability overlap" for the statement I guess is one way
of putting it. Another way of putting it
(described

here)
is that by adding specific information "You've effectively told people about one individual, not told
them that one of your children is a member of a category."

**UPDATE**: This solution (as per the puzzle's creator) is controversial. The puzzle is
discussed

here, and at the
end of the discussion, includes Gary Foshee's response to the criticism of his answer. He admits "If you
start putting in factors about how the children were chosen, from which set, then yes there is an argument
the answer could be different. It's a very tricky and controversial subject."

And in this

math bulletin, the
author was even more critical, concluding "the question that Foshee actually answered was:

*Of all
two-child families with at least one child being a boy born on a Tuesday, what proportion of those
families have two boys?* The correct answer to the question he actually posed is P = 1/2."

We'll take the middle ground here and say the answer is controversial. :-)