What is the probability that both children are boys if at least one is a boy born on a Tuesday?
Have a look and count the number of succesful outcomes compared to the total number:
If you correct for biological factors, however, the answer may be skewed in either direction. Perhaps boys are a little more likely than girls, so I have heard.
If we only dealt with gender, not the day of week, your figure would have been correct since the table would then simply be:
The two things that confuse our intuitions are:
It is counter intuitive that someone would NOT mention which kid (the oldest, the youngest) which allows for the overlapping areas in the two tables.
It is counter intuitive that the day of week plays the role that it does.
This is another twist on the classic Boy or Girl paradox (Wikipedia). This variant even has its own section on the Wikipedia page.
You do have to include the information about Tuesday. Let $A$ be the event both children are boys, and let $B$ be the event at least one was a Boy born on a Tuesday.
$$ P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{(1/2)^2\cdot (1-(6/7)^2)}{1-(1-(1/2)(1/7))^2}\neq \frac13 $$