SOLUTION: on the lot at honest al's used yugo superstore there are 60 yugos. 20 of the yugos have bad engines, 25 have bad transmissions, 15 have bad engines and bad transmissions. if one yu

Question 112414: on the lot at honest al's used yugo superstore there are 60 yugos. 20 of the yugos have bad engines, 25 have bad transmissions, 15 have bad engines and bad transmissions. if one yugo is selected, find the probability that it has a bad engine or bad transmission.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There is a question of semantics in this problem. The straight-forward answer is that there are a total of 45 Yugos that have either a bad engine or a bad transmission, (20 + 25). So the probability that any selected car will have either a bad engine or a bad transmission is .

On the other hand, the "or" in "bad engine or bad transmission" could be an exclusive or. In other words, meaning a bad engine or bad transmission but not both. If this is the case, then you would have to say that of the 20 cars with bad engines, 15 of them also have a bad transmission, so there are only 5 (20 - 15) that only have a bad engine. Likewise, there are only 10 (25 - 15) that only have a bad transmission. This is 15 (5 + 10) possibilities out of the 60 total cars: .

Common usage of the word "or," which is the inclusive sense as used in the first solution, would lead me to believe that the first answer is the correct one, but the inclusion of the fact that "15 have bad engines and bad transmissions," a fact that is unnecessary unless the "or" were to be taken in the exclusive sense, makes me think the second answer is the desired one. Ask your instructor what was meant.

Hope this helps,
John
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