A scientist is working on a new test for cotton allergies. She knows that 2.5% of all the students at Annie's school are allergic to cotton. For those who are allergic, 80% test positive and 20% test negative. For those who are not allergic, the test shows 10% positive and 90% negative.Use Bayes's theorem to find the probability that a student at Annie's school is allergic to cotton, given that the test results are positive.

Bayes Theorem: P(A l B)= [P(B I A) x P(A)]/ P(B)

Question

A scientist is working on a new test for cotton allergies. She knows that 2.5% of all the students at Annie's school are allergic to cotton. For those who are allergic, 80% test positive and 20% test negative. For those who are not allergic, the test shows 10% positive and 90% negative.Use Bayes's theorem to find the probability that a student at Annie's school is allergic to cotton, given that the test results are positive. 

Bayes Theorem: P(A l B)= [P(B I A) x P(A)]/ P(B)