HardBiologyHigh School (11–12)Human BodyNumerical

A health worker explains that the failure rate of a method is the chance of a pregnancy in one…

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A health worker explains that the failure rate of a method is the chance of a pregnancy in one year, and that the chance over many years is larger. She uses two methods from a WHO table of typical use: the male condom, with $13$ pregnancies in the first year among $100$ users, and the copper releasing IUD, with $0.8$ . She assumes that the chance is the same in every year and that the years are independent of one another.

What is the chance of at least one pregnancy in $5$ years of using the condom?

What is the chance in $10$ years of using the condom?

What is the chance in $10$ years of using the IUD?

Which method gives the smaller chance in $10$ years, and why is the chance after $10$ years larger than after $5$ years?

Need a reminder? The key ideaShow

A failure rate $f$ is the number of pregnancies in the first year among $100$ users. Among $n$ couples, about $\dfrac{n \times f}{100}$ pregnancies are expected in a year. The chance of at least one pregnancy in $t$ years is $1 - (1 - f/100)^t$ . Only the condom, among the methods of this chapter, protects against STIs. Vasectomy and tubectomy are terminal methods.

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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