# Math Chat

Math Chat

Frank Morgan

Professor of Mathematics, Wiliams College

If a Ball Goes Up, When Must It Come Down?

Thanks for the tremendous response to the Father's Day Math Chat column June 14. The answer appears below, along with a new challenge question. But first, here's a copy of the last question for those who didn't see it:

Challenge question From Father's Day

Suppose every husband and wife keep having children until they have a girl and then stop. Assuming boys and girls are equally likely, will this produce more baby boys or more baby girls in the whole population?

Answer:

You might think more girls, since every couple has a girl. Or you might think more boys, since many a couple has lots of boys before having one girl. Actually, these two effects balance exactly, and one should expect equal numbers of boys and girls.

The first year, couples expect half girls and half boys. The couples with boys try again, and the second year they expect half girls and half boys (since odds are unaffected by what has gone before). Similarly, every year the remaining couples expect half girls and half boys.

A shorter answer is that at every birth, no matter the history, a boy or a girl is equally likely, so one expects equal numbers of each.

Winners

Winning answers for the last math chat came from: Timothy Clark, Aubrey Dunne, William Foster, Charles Gahr, Lawson and Priscilla Harris, Jerry Heckmann, Robin Konicek, William Malkames, Mike Moxcey, Jerry Alan Scripps, Deborah Tingle.

New challenge question

If you throw a ball in the air, it takes the same amount of time to go up as to come down, neglecting air friction. What if you take friction into account?

* Answers will appear in a future Math Chat column next to the Monitor's Friday crossword.

Send answers, comments and new questions to:

Math Chat

Bronfman Science Center

Williams College

Williamstown, MA 01267

or e-mail:

Frank.Morgan@williams.edu

The best submissions will receive a copy of the book "Flatland," which explains higher dimensional spaces.