Bayes theorm with one simple example?

Answer 1

First P(E|F) means the probability of E given F. Now, Bayes theorem gives us a way of calculating P(E|F) if we know P(F|E).

P(F|E) =(E|F)P(F) divided by

P(E|F)P(F) + P(E|F')P(F')

E = the event that an anabolic steroid detection test gives a positive result

F = the event that the athlete uses steroids
then
P(E|F) = probability that the test is positive for an athlete who uses steroids.
P(F|E) = probability that an athlete uses steroids given that the test is positive.

A drug test will detect steroid use meaning it show positive for an athlete who uses steroid 95% of the time. A Rugby player has just tested poositive. The probability that he uses steroids is:

P(E|F) = 0.95 P(E|F') = 0.15 P(F) = 0.1 P(F') = 0.9

P(E|F)=(0.95)(0.1) divided by

(0.95)(0.1) + (0.15)(0.9)