A family has two children. Given that at least one of the children is a boy who was born on a Tuesday, what is the probability that both children are boys?
The day of birth is independent of the gender
P(both are boys $\mid $ at least one boy) = P(both are boys) / P(at least one boy)
$= P(\text {both are boys}) / [1 – P(\text{both are girls}$)]
$= 0.5^2/(1-0.5^2)$
$= 0.25/0.75$
$= 0.3333$
Best Answer
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.