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Math Help - Probability Question - Can't figure out

  1. #1
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    Probability Question - Can't figure out

    This seems like it should be easy but I can't get my mind around it:

    "Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

    Any help would be appreciated, even if it's just a starting point.

    Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by aliveiam View Post
    This seems like it should be easy but I can't get my mind around it:

    "Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

    Any help would be appreciated, even if it's just a starting point.

    Thanks!

    If I understand this correctly....
    Let R=red and C=convertible. You want

     P(R|C) ={P(RC)\over P(C)} ={.05\over .2} ={1\over 4}.
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  3. #3
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    Quote Originally Posted by aliveiam View Post
    This seems like it should be easy but I can't get my mind around it:

    "Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

    Any help would be appreciated, even if it's just a starting point.

    Thanks!
    Suppose there were 100 cars at the dealership. Since 80% of 100= 80 are NOT convertibles, 20 are convertibles. There are 5% of 100= 5 red convertibles so 5/20= 0.25 or 25% of the convertibles are red. The probability that a convertible is red is 0.25.
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