Probability and Baby Blues

[Photo by audi_insperation.]

[In The Birthday Surprise, Alex discovered her family was expecting a new member…]

What will the baby look like, Alex wondered. “Dad, is there any way to tell whether the baby will have blue eyes like I do, or brown like the rest of the family?”

Dr. Jones shuffled the papers on his desk and found a blank page. “Over 100 years ago, the Austrian monk Gregor Mendel studied genetics, or how various traits are passed down from one generation to another.” He began to draw a diagram as he talked.

Brown and Blue Eyes

“Mendel analyzed pea plants, but the principles he discovered apply to many living things — including people,” Dr. Jones explained. “This is a Punnett square, which shows all the possible combinations of a pair of genes.”

“Let me guess,” Alex said. “Mendel planted a huge garden and used the Law of Large Numbers?”

Her father laughed. “Well, he may have done it the other way around. When he published his data, it matched his theory so well that at least one scientist has suggested that he decided the percentages he wanted and tweaked the numbers until they fit . . . Here we have the brown-eyed (B) or blue-eyed (b) genes that you kids could inherit from your mother and me.”

“How do you know what your genes are?” Alex asked.

“Maria and I both have brown eyes, but we have a blue-eyed child. Since brown eyes are dominant, BB or Bb genes will make brown eyes.” He pointed to the chart. “Only a bb combination would give you your blue eyes. And only two Bb parents can have brown eyes and still make a baby with bb genes.”

And a Puzzle

“Now, Alex, count out the chances,” Dr. Jones said. “What is the probability of a blue-eyed baby?”

Alex pouted. “None, since I’ve already used the blue-eyed genes. I guess this baby will have to have brown eyes.”

  • Was Alex right?
    (Hint: No, but why not?)
  • Many homeschoolers have large families. What is the probability of two brown-eyed parents having four blue-eyed children?

To Be Continued…

Read all the posts from the July/August 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.

8 thoughts on “Probability and Baby Blues

  1. “What is the probability of two brown-eyed parents having four blue-eyed children?”

    To answer this question, one must know the size of the family you’re interested in. Does the family have two children (in which case the probability of four blue-eyed children is obviously zero)? Four children? Twelve? …

    (My guess is that you intended the question to mean four blue-eyed children among four children.)

    Also, are we to assume that the brown-eyed parents are of hybrid genotypes (Bb) like Alex’s parents?


    1. Good point, Eric! I was assuming any brown-eyed parents — although Joshua challenges my assumptions, and he sounds like he knows more about it than I do. I was also assuming a 4-child family, although that was rather silly of me. There are a few very large homeschooling families in my area, so I should have realized that 4 children was just the beginning.

      Of course, any larger family could have 4 (or more) blue-eyed children — and the more children one has, the better the chance for at least some blue eyes.

  2. Mendel was awesome! Even though no one paid attention to his findings at the time, and he left his work to resume more “religious” studies, he is called the “Father of Genetics”. Have you tried working a problem with 2 variables? Try blue eyes and red hair! You have a 1/16 chance of getting that combo if both parents are heterozygous.

  3. I like the general idea of the lesson. However, in real life, the situation might be a lot more complicated, so maybe it’s not the best example. A blue-eyed kid, with brown-eyed parents, could easily have a recessive green, hazel, or even brown eye gene. This might give children the false impression that everything’s more predictable than it really is.

  4. Most real-life situations are more complicated than can be described in a short blog post, aren’t they? I never heard before that there could be a recessive brown eye gene!

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