Question

Please provide steps and explanations. Thank you!

Dr. John’s favorite pizza flavors are broccoli and sausage. Let B be the event that he orders broccoli on an odd day and S represents the event that he orders sausage on an even day. During a random week, the probability that Dr. John will order broccoli pizza on an odd day is 0.55, the probability that he will order a sausage pizza on an even day is 0.84, and the conditional probability that he orders broccoli pizza on an odd day, given that he ordered sausage pizza on an even day is 0.4. What is the probability that Dr. John will order a sausage pizza on an even day given that he ordered broccoli pizza on an odd day?

Answer 1

P[ Dr. John will order broccoli pizza on an odd day ] = 0.55

P[ he will order a sausage pizza on an even day ] = 0.84

P[ he orders broccoli pizza on an odd day |  he ordered sausage pizza on an even day ] = 0.4

P[ he orders broccoli pizza on an odd day |  he ordered sausage pizza on an even day ] = P[ he orders broccoli pizza on an odd day and he ordered sausage pizza on an even day ] / P[ he will order a sausage pizza on an even day ]

0.4 =  P[ he orders broccoli pizza on an odd day and he ordered sausage pizza on an even day ] / 0.84

P[ he orders broccoli pizza on an odd day and he ordered sausage pizza on an even day ] = 0.4/0.84

P[ he orders broccoli pizza on an odd day and he ordered sausage pizza on an even day ] = 0.4762

We need to find

P[ Dr. John will order a sausage pizza on an even day | he ordered broccoli pizza on an odd day ] =  P[ he orders broccoli pizza on an odd day and he ordered sausage pizza on an even day ] / P[ Dr. John will order broccoli pizza on an odd day ]

P[ Dr. John will order a sausage pizza on an even day | he ordered broccoli pizza on an odd day ] = 0.4762 / 0.55

P[ Dr. John will order a sausage pizza on an even day | he ordered broccoli pizza on an odd day ] = 0.8658