HardBiologyHigh School (11–12)Human BodyNumerical

In a made-up model for learning, one exposure to a certain infection has a 4% chance of passing it…

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

In a made-up model for learning, one exposure to a certain infection has a $4\%$ chance of passing it on when no condom is used. A person is exposed $30$ times. The model takes it that a condom cuts the chance in one exposure by $80\%$ . The numbers are not data for any real infection.

What is the chance of at least one infection in $30$ exposures, if no condom is ever used?

What is the chance, if a condom is used in half of the $30$ exposures? Treat each exposure as having the average chance, which is $4\% \times (1 - 0.8 \times 0.5)$ .

What is the chance, if a condom is used every time?

By how many percentage points does the use of a condom every time lower the chance, compared with no condom?

Need a reminder? The key ideaShow

NCERT lists eight sexually transmitted infections: gonorrhoea, syphilis, genital herpes, chlamydiasis, genital warts, trichomoniasis, hepatitis-B and HIV (AIDS). Except for hepatitis-B, genital herpes and HIV, the others are completely curable if detected early. Those three can also spread by needles, by blood and from mother to foetus. If one exposure has chance $q$ , then the chance of at least one infection in $n$ exposures is $1 - (1 - q)^n$ .

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.

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