HardBiologyHigh School (11–12)Human BodyNumerical

A fertility clinic uses a made-up model to explain how chances add up…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A fertility clinic uses a made-up model to explain how chances add up. In the model, each cycle of an assisted reproductive technology gives a pregnancy with a chance of $30\%$ , and each cycle is independent of the others. The numbers are not data for any real clinic. A counsellor wants to answer three questions for a couple who are thinking of several cycles.

What is the chance of at least one pregnancy in $3$ cycles?

What is the chance of at least one pregnancy in $5$ cycles?

What is the smallest number of cycles for which the chance of at least one pregnancy is $90\%$ or more?

Is the chance after $10$ cycles exactly $100\%$ ?

Need a reminder? The key ideaShow

A zygote divides, and the number of blastomeres doubles at each division: $2^n$ after $n$ divisions. A zygote or an embryo of up to $8$ blastomeres goes into the fallopian tube (ZIFT). An embryo of more than $8$ blastomeres goes into the uterus. In GIFT, the ovum of a donor goes into the fallopian tube. If each cycle succeeds with chance $s$ , the chance of at least one success in $n$ cycles is $1 - (1 - s)^n$ .

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.

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