Question

Suppose that 2% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive? Round your answer to the nearest tenth of a percent.

Answer 1

To answer this you will find what 75% of the 2% of the student is. To calculate this, you will multiply 75% (0.75) and 2% (0.02). The answer is 0.015 which rounds to 0.02 chance. As a percent it is a 1.5% probability.

Answer 2

Answer: Probability of getting a student in the school has head lice given that the test came back positive is 0.058.

Explanation:

Since we have given that

Let E be the event that the student actually having head lice.

Let A be the event that the report shows positive.

Since there are 2% of the students in a school having lead lice.

P(E) = 0.02

P(E')=1-0.02=0.98

Similarly, the probability that the test for head lice is accurate = 75% of the time.

So,
`P(A\mid E)=75\%=0.75\\\\Similarly,\\\\P(A\mid E')=1-0.75=0.25`

We need to find the probability that a student in the school has head lice , given that the test came back positive.

So, By using Bayes Theorem, we get that

`P(E\mid A)=(P(A\mid E).P(E))/(P(A\mid E).P(E)+P(A\mid E').P(E'))\\\\P(E\mid A)=(0.02* 0.75)/(0.02* 0.75+0.98* 0.25)\\\\P(E\mid A)=(0.015)/(0.015+0.245)\\\\P(E\mid A)=(0.015)/(0.26)\\\\P(E\mid A)=0.0576\approx 0.058=5.8\%`

Hence, Probability of getting a student in the school has head lice given that the test came back positive is 0.058.