The probability that Trevor eats breakfast is 0.4. The probability that Trevor g

Question

The probability that Trevor eats breakfast is 0.4. The probability that Trevor goes to work on time is 0.6. The probability that Trevor both eats breakfast and gets to work on time is 0.2. Answer the following questions using knowledge of conditional probability. (You must show your work to earn credits. Any answer with no work will receive zero credit.) On a random day that trevor eats breakfast, what is the probability that he is on time to work? On a random day that Trevor is on time to work, what is the probability that he eats breakfast? On a random day that trevor does not eat breakfast, what is the probability that he is on time to work? On a random day that Trevor is not on time to work, what is the probability that he eats breakfast?

Explanation / Answer

P(eats breakfast) = 0.4

P(goes work on time) = 0.6

P(eats breakfast and goes work on time) = 0.2

1) P(goes work on time | eats breakfast) = P(eating breakfast and goes work on time) / P(eats breakfast)

                                                                = 0.2 / 0.4

                                                                = 0.5

2) P(eats breakfast | goes work on time) = P(eats breakfast and goes work on time) / P(goes work on time)

                                                                = 0.2 / 0.6

                                                                = 0.33

3) P(goes work on time) = P(goes work on time and does not eat breakfast) + P(goes work on time and eats breakfast)

or, 0.6 = P(goes work on time and does not eat breakfast) + 0.2

or, P(goes work on time and does not eat breakfast) = 0.4

P(does not eat breakfast) = 1 - P(eats breakfast)

                                         = 1 - 0.4

                                         = 0.6

P(goes work on time | does not eat breakfast) = P(goes work on time and does not eat breakfast) / P(does not eat breakfast)

                                                                         = 0.4 / 0.6

                                                                         = 0.67

4) P(eats breakfast) = P(eats breakfast and does not go work on time) + P(eats breakfast and goes work on time)

or, 0.4 = P(eats breakfast and does not go work on time) + 0.2

or, P(eats breakfast and does not go work on time) = 0.2

P(does not go work on time) = 1 - P(goes work on time)

                                              = 1 - 0.6

                                               = 0.4

P(eats breakfast | does not go work on time) = P(eats breakfast and does not go work on time) / P(does not go work on time)

                                                                       = 0.2 / 0.4

                                                                       = 0.5

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