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# Tree diagrams for conditional probabilities

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Ed's Tires and Brakes has two locations, one on the northwest side of town and one on the southeast side of town. At both locations are performed routine tire repairs and rotations, as well as expensive brake repairs. This past week, 80% of the cars serviced at Ed's were serviced at the northwest location, while 20% of the cars were serviced at the southeast location. (No car was serviced at both locations.) Brake repairs were more typical at the northwest location than at the southeast location: 55% of the cars at the northwest location required brake repairs, while 25% of the cars at the southeast location required brake repairs.
Let N denote the event that a randomly chosen car (taken to Ed's in the past week) was serviced at the northwest location and denote the event that a randomly chosen car was serviced at the southeast location. Let B denote the event that a randomly chosen car required brake repairs and denote the event that a randomly chosen car did not require brake repairs.
Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.

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The solution shows detailed steps of calculating the conditional probabilities.

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## Tree Diagrams for Conditional Probabilities

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Tree diagrams for conditional probabilities
A course in statistics is one of the most difficult at the local university. Because of this, for the past decade the university has arranged for teaching assistants to hold frequent discussion sessions as part of the course. Since the inception of the discussion sessions, of the students enrolled in the course regularly attended the sessions, and the other did not. Students regularly attending the sessions have performed better than those not regularly attending. In particular, of the students regularly attending the sessions received a grade of "B" or higher in the course, while only of the students not regularly attending the sessions received a grade of "B" or higher in the course.
Let denote the event that a randomly chosen student (enrolled in the course) regularly attended the discussion sessions, and let denote the event that a randomly chosen student did not regularly attend the discussion sessions. Let denote the event that a randomly chosen student received a grade of "B" or higher in the course, and let denote the event that a randomly chosen student did not receive a grade of "B" or higher in the course.
Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.

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