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