September 01, 2018 at 11:30PMTo remind you, here’s the problem:
On the first day of a new job, a colleague invites you for a barbecue. As the two of you arrive at his home, a young boy throws open the door to welcome his father. “My other two kids will be home soon!” remarks your colleague.
Waiting in the kitchen while your colleague gets some drinks from the basement, you notice a letter from the principal of the local school tacked to the noticeboard. “Dear Parents,” it begins, “This is the time of year when I write to all parents, such as yourselves, who have a girl or girls in the school, asking you to volunteer your time to help the girls’ soccer team.” “Hmmm,” you think to yourself, “clearly they have at least one of each!”
This, of course, leaves two possibilities: two boys and a girl, or two girls and a boy. Are these two possibilities equally likely, or is one more likely than the other?
Solution:
The father has 3 children. The child at home is a boy. The other two are either two girls or a girl and a boy.
Since we know the child at home is a boy, we’ll put boy in one slot of our chart.
B X X.
So what are the possibilities for the other two children?
B G G
B B G
B G B
Two out of the three (equally likely possibilities) involve a boy and a girl, so there is a 2/3 chance he has 1 girl, and a 1/3 chance he has 2 girls.
Answer: One is more likely than the other.
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