probability in math

Question

the probability of eating pizza for dinner on friday is 65% and the probability of going to bed early on friday is 58%. the probability of going to bed early on friday given that you eat pizza for dinner is 82% what is the probability of eating pizza on friday given that you go to bed early on friday

Answer 1

P(pizza) = P(P)

P(bed early) = P(B)

Wr can express the percentages as decimals:

For example, 50% = 0.5

If independent,

P(P AND B) = P(P)*P(B) = (0.58)(0.65) = .377

P(B given P) = P(P AND B)/P(P) = 0.377/0.65 = 0.58

However, the probability we are given is higher at 82%, so these must be dependent events.

To find the probability of both, work backwards:

0.82 = P(P AND B)/P(P) =P(P AND B)/0.65

P(P AND B) = (0.82)(0.65) = 0.533

Then,

P(P given B) =

P(P AND B)/P(B) = (0.533)/(0.58) = 0.92

Hope that helps!