Comment and Answers

Hi class!


Reading through your responses I am quite impressed. Many of you took different approaches to solving the questions as well as debated with each other how they went about coming up with the answers. Well done! Here are the answers to the problems. Again, I am not marking you based on if your answer is correct but how you went about coming up with your answer.
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Problem 1 Solution

The position in line that gives you the best chance of being the first duplicate birthday is 20th.


Problem 2 Solution

We assume that each birth is an independent event, for which the probability of a boy is the same as the probability of a girl. There are, then, three possibilities for your colleague's family, all equally likely:

•Boy, Boy, Girl

•Boy, Girl, Boy

•Boy, Girl, Girl

Therefore there is a 2/3 chance that the colleague has two boys and a girl, and a 1/3 chance he has two girls and a boy.