A couple have five children, and all five are girls…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A couple have five children, and all five are girls. They ask whether this means that they are more likely to have another girl, because they seem to produce only girls.
- What was the chance that five children, chosen in advance, would all be girls?
- What is the chance that the sixth child is a girl?
Need a reminder? The key ideaShow
In humans and the fruit fly, the father decides the sex, because half the sperm carry X and half carry Y. In birds the egg decides, because the female is ZW. In the honey bee, a fertilised egg (2n = 32) becomes a female and an unfertilised egg (n = 16) becomes a drone.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Five girls out of five children.
Plan. The sex of each child is decided by the sperm of the father, and each sperm is an independent event.
Step 1. (a) The chance for five girls is .
Step 2. (b) The sixth child is a girl or a boy with a chance of one half each. The chance of a girl is .
Answer: ; .
Check. Five girls in a row is rare, but one such family in is expected by chance.
Watch out. Earlier children do not change the chance for the next child. The father's sperm carry X and Y in equal numbers every time.
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