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 …

Question

asked Sep 23, 2022 203k views

1 Answer

David Corsalini · Answer 1 · 2022-09-27T13:43:54+0000

Answer:

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