Suppose 90% percent of kids who visit a doctor have a fever, and 45% of kids with a fever have sore throats. What’s probability that a kid who goes to the doctor has a fever and a sore throat?

**Solution**

The general multiplication rule for compound events is given below.

P(A and B) = P(A) * P(B│A)

To find the probability that a kid who goes to the doctor has a fever and a sore throat, break down the probability into simpler events.

The probability that a kid who goes to the doctor has a fever is P(fever) = 0.9.

Find the probability that a kid has a sore throat, given that he has a fever.

P(sore throat │fever ) = 0.45

Use the general multiplication rule to find the probability that a kid who goes to the doctor has a fever and a sore throat.

P(fever and sore throat) = P(fever) * P(sore throat │ fever)

= 0.9 * 0.45

= 0.405