Question

During a flu epidemic, 35% of the school's students have the flu. Of those with the flu, 90% have high

temperatures. However, high temperatures are possible for people who do not have the flu. It is estimated that
12% of those without the flu have high temperatures.
If a student has a high temperature, what is the probability that the student has the flu?

Answer 1

Answer: 0.8015

Explanation:

Let F= event that a person has flu

H= event that person has a high temperature.

As per given,

P(F) =0.35

Then P(F')= 1- 0.35= 0.65 [Total probability= 1]

P(H | F) = 0.90

P(H|F') = 0.12

By Bayes theorem, we have

`P(F|H)=(P(F)*P(H|F))/(P(F)*P(H|F)+P(F')*P(H|F'))\\\\=(0.35*0.90)/(0.35*0.90+0.65*0.12)\\\\=(0.315)/(0.315+0.078)\approx0.8015`

Required probability = 0.8015