A couple plans two children. The chance that a child is a girl is 12 at each birth, and the births…
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 plans two children. The chance that a child is a girl is at each birth, and the births are independent.
- What is the chance that the first child is a girl?
- What is the chance that both children are girls?
- What is the chance that at least one child is a boy?
Need a reminder? The key ideaShow
Fertilisation takes place in the ampulla and gives a zygote with chromosomes. Cleavage gives cells after divisions, with no growth of the embryo. The morula has to cells. The blastocyst has a trophoblast and an inner cell mass. The ovum always carries X, and a sperm carries X or Y with equal chance. The trophoblast attaches to the endometrium in implantation.
The worked solution
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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. Chance of a girl: at each birth.
Plan. List the equally likely pairs: boy-boy, boy-girl, girl-boy, girl-girl.
Step 1. First child. The ovum carries X. The sperm carries X or Y with equal chance, so the chance of a girl is .
Step 2. Both girls. One pair out of : .
Step 3. At least one boy. Three pairs out of : .
Answer: ; ; .
Check. The chances of two girls and of at least one boy add up to .
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