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

0.8015 = 80.15% probability that the student has the flu

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has high temperature.

Event B: Has the flu

Probability of a student having high temperatures:

90% of 35%(have the flu)

12% of 100 - 35 = 65%(do not have the flu). So

`P(A) = 0.9*0.35 + 0.12*0.65 = 0.393`

Probability of having high temperatures and the fly?

90% of 35%, so

`P(A \cap B) = 0.9*0.35 = 0.315`

If a student has a high temperature, what is the probability that the student has the flu?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.315)/(0.393) = 0.8015`

0.8015 = 80.15% probability that the student has the flu