Respuesta :
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: Probability of getting a student in the school has head lice given that the test came back positive is 0.058.
Step-by-step 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, [tex]P(A\mid E)=75\%=0.75\\\\Similarly,\\\\P(A\mid E')=1-0.75=0.25[/tex]
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
[tex]P(E\mid A)=\dfrac{P(A\mid E).P(E)}{P(A\mid E).P(E)+P(A\mid E').P(E')}\\\\P(E\mid A)=\dfrac{0.02\times 0.75}{0.02\times 0.75+0.98\times 0.25}\\\\P(E\mid A)=\dfrac{0.015}{0.015+0.245}\\\\P(E\mid A)=\dfrac{0.015}{0.26}\\\\P(E\mid A)=0.0576\approx 0.058=5.8\%[/tex]
Hence, Probability of getting a student in the school has head lice given that the test came back positive is 0.058.
