Archive for December 23rd, 2008

Conundrum: Blue Gene Baby

Tuesday, December 23rd, 2008

I had the pleasure of observing a science teacher teach a fantastic lesson on genetics last week, and it got me thinking about the mathematics behind eye color. This Conundrum will be purely a probability question (two, actually), so I apologize in advance for over-simplifying the science.

Assume that everyone has two genes that determine eye color. For the sake of the math, we will stipulate that each gene must be either brown or blue. An individual inherits one gene from each parent. A parent will pass on one of his or her own two genes with equal probability.

Brown is dominant, which means that if an individual has one brown gene and one blue gene, then the individual will have brown eyes. An individual will also have brown eyes if both genes are brown. Only an individual with two blue genes will have blue eyes.

Now imagine this hypothetical scenario: Susan and David are a married couple, and both have brown eyes. David’s father had blue eyes, and his mother had brown eyes. Susan’s parents both had brown eyes, but her brother Bill has blue eyes. Susan and David are expecting their first child, baby Jason.

Question 1: What are the chances that Jason will have blue eyes?

Question 2: Suppose Jason had brown eyes. Susan and David are now expecting a second child, baby Ian. What are the chances that Ian will have blue eyes?

UPDATE: Both questions answered correctly by Micah. See comments for answers and discussion.