Embed Notice

Yes, if someone filters a set of paired results based on known outcomes, that changes the odds of your guess; that's why the monty hall problem works. But this problem is not that. There are not 100 mothers with a random distribution of two children, of which those with two daughters have been eliminated. There is one mother, and the chances of her child being either sex is 50/50.

Look, even if we don't know what day of the week the daughter was born on, we know she was born on a day of the week, so you always can go ahead and draw your weekdays in the table and scratch out the "day X" column even if 'Tuesday' isn't explicitly mentioned in the problem. So we have changed the probability from 66% to 51% just by drawing the table differently with no additional information in the problem. Obviously that outcome is ridiculous. And why stop at day of the week? We also know she was born on a particular date of the year, so you could draw 365 dates into the table and scratch out the 'date x' column. It's an example of statistical modeling where what you choose to model determines the probability space of the model, it doesn't translate to real-world outcomes.