Suppose that 1% 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?,
Accepted Solution
A:
Answer: There is a 2.9% chance that a person has head lice given that the test is positive. (I know that sounds very low, but watch the math)
Imagine there are 10,000 students in the school. If 1% have lice, that makes 100 students that have it and 9,900 that don't.
Assume the test was given to all students. Out of the 100 that have lice, only 75 would get a positive test because it is only 75% accurate.
Now, out of the 9,900 student who don't have lice, 25% of them would get a positive test, because the test is only 75% accurate. That is 2,475 false positive tests!!!
So we had a total of 2,550 positive tests, but only 75 of those students actually have lice. 75 out of 2550 is 2.9%.