Pick a random family uniformly among all families with
exactly 2 children of which one (at least) is a girl. What is the likelihood
that the chosen family has 2 girls? Under the usual assumption of gender
uniformity at birth, the answer is 1/3, not 1/2 as many people initially
assume. This is fairly well known, but is still a useful warm-up.
What if we pick a random family among all families with exactly 2 children, at least one of which is a girl born on a Tuesday?
Most people assume that the day of week the birth took place on makes no difference. They're wrong. The likelihood of 2 girls in this new scenario is now a lot closer to 1/2 than it is to the original 1/3. It's a useful exercise to explain, intuitively, why that is.
It's best to explicitly state that twins are to be ignored here. It's also better to phrase the question precisely as sampling from a well-defined sample space, rather than the usual pitfall-laden tales of "you meet a stranger and they tell you they have two children and at least one is a girl born on a Tuesday".
(Analysis of this problem shall be posted on the next Monthly Digest)
What if we pick a random family among all families with exactly 2 children, at least one of which is a girl born on a Tuesday?
Most people assume that the day of week the birth took place on makes no difference. They're wrong. The likelihood of 2 girls in this new scenario is now a lot closer to 1/2 than it is to the original 1/3. It's a useful exercise to explain, intuitively, why that is.
It's best to explicitly state that twins are to be ignored here. It's also better to phrase the question precisely as sampling from a well-defined sample space, rather than the usual pitfall-laden tales of "you meet a stranger and they tell you they have two children and at least one is a girl born on a Tuesday".
(Analysis of this problem shall be posted on the next Monthly Digest)