At Jaxlyn’s Garage, 200 cars were inspected and worked on. There were 92 cars that needed new brakes, 136 cars that needed a new
alternator, and 24 cars that needed neither repair. Part A: Determine the probability of a car needing both repairs. Part B: Determine the probability of a car needing an alternator, but not new brakes.
2 answers:
Answer:
(a) 13/50
(b) 21/50
Step-by-step explanation:
We need to make a Venn Diagram (see the attachment).
Notice that the two circles are "need a brake" and "need an alternator". The intersection is simply the cars that need both repairs.
(a) Let's say b is the number of cars that need both repairs. 92 is the number of cars that need a new brake, but that also includes the cars that need both repairs. The number of cars that only need brakes is 92 - b. Similarly, the number of cars that only need an alternator is 136 - b.
We add up 92 - b, b, and 136 - b to get the number of cars that need repairs, and we set this equal to 200 - 24 (because 24 cars don't need repairs, 200 - 24 are the total number of cars that do):
(92 - b) + b + (136 - b) = 176
228 - b = 176
b = 52
52 cars need both repairs, so the probability that a car needs both repairs will be 52/200 = 13/50.
(b) The number of cars that need an alternator but not new brakes is 136 - b = 136 - 52 = 84 cars. Then the probability that a car needs an alternator but not brakes is 84/200 = 21/50.
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