Probability, studies

Question

The probability that Jon studies and passes his math test is 13/16. If the probability that Jon studies is 19/20, find the probability that Jon passes his test, given that he has studied

Answer 1

P(Studies and Passes) = 13/16

P(Studies) = 19/20

P(Passes | Studies) = ???

We need to find the conditional probability.

P(Passes | Studies) = P(Studies and Passes) ÷ P(Studies) = (13/16) ÷ (19/20) = (13/16)(20/19) = 65/76

The probability that Jon passes his math test given the fact that he studied is 65/76.

Answer 2

S= studies

P = passes

P(S^P) = 13/16

P(S) = 19/20

P(P/S) = ??

P(S^P) = P(P/S)P(S)

13/16 = P(P/S)(19/20)

P(P/S) = (13/16)/(19/20) = 13/16 x 20/19 = 13/4 x 5/19 = 65/76

Probability that he passes given that he studies = 65/76