Question

Jane is the star swimmer at Tumbleweed College, Nevada. But Tumbleweed rarely hosts swim competitions on account of their poorly funded swim program. In fact, only 22 percent of Jane's swim competitions are at Tumbleweed, while the remaining 78 percent are held at the rival college in Carson City. She wins 65 percent of the races at Tumbleweed, but only 55 percent of the competitions held at Carson City. Jane in fact won her most recent competition. How probable is it that it was held at Tumbleweed given that she won, that is, what is P(H1|E)? identify values of the four terms P(H1) = P(H2) = PIE | H1) = PIE|H2) = plug in the values, calculate value of: P(H1E) =

This problem has to be solved using Baye's theorem. Please justify the four terms in solution. Thank you! :)

(this is philosophy btw)

Answer 1

H1 : competition at tumbleweed

H2 : competition at carson

E : she won

given :

P(H1) = 0.22

P(H2) = 0.78

P(E | H1) = 0.65

P(E | H2) = 0.55

P(E) = P(E | H1)*P(H1) + P(E | H2)*P(H2) = 0.65*0.22+0.55*0.78 = 0.572

P(E) = 0.572

to find :

P(H1 | E)

bayes theorem :

P(BA) P(A) P(A/B) = P(B)

so,

P(H1 | E) = P(E | H1)*P(H1) / P(E)

P(H1 | E) = 0.65*0.22 / 0.572 = 0.25

P(H1 | E) = 0.25

P.S. (please upvote if you find the answer satisfactory)