Question

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?

Answer 1

P( lice ) = .01

P( test positive | lice ) = .75

Find probability
P ( lice | test positive)

Answer 2

Let's derive a rule

P(A | B)
= P(A & B) / P(B)

now P(A&B) = P(A) * P(B | A )
so lets substitute that

P(A|B) = P(A) P(B|A) / P(B)

P ( lice | test pos. ) = P(lice) * P ( test pos. | lice ) / P( test pos.)

Answer 3

does that make sense so far

Answer 4

yea, i got to that point but after that i keep getting .75 as an answer

Answer 5

it might be easier to use a tree diagram

Answer 6

it says the test is accurate 75% of the time

there are two types of 'accuracy.
if someone has lice then it tests positive 75% of the time
if someone does not have lice then it tests negative 75% of the time