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Math Help - Conditional probability question

  1. #1
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    Conditional probability question

    On a wintry day, a salesman randomly chooses to drive to 2 of the following three cities: Los Angeles, San Francisco, and Sacramento.
    The probability of rain on a wintry day is:
    1/3 in San Francisco
    1/4 in Sacramento
    1/6 in Los Angeles
    He returned home with wet clothes.
    What is the probability he had visited Los Angeles?
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  2. #2
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    Re: Conditional probability question

    Quote Originally Posted by msokol89 View Post
    On a wintry day, a salesman randomly chooses to drive to 2 of the following three cities: Los Angeles, San Francisco, and Sacramento.
    The probability of rain on a wintry day is:
    1/3 in San Francisco
    1/4 in Sacramento
    1/6 in Los Angeles
    He returned home with wet clothes.
    What is the probability he had visited Los Angeles?
    \frac{\frac{1}{3} \times \frac{1}{6}}{\frac{1}{3} \times \frac{1}{6} + \frac{1}{3} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{4}} = ....

    Your job is to review conditional probability so that you understand where this expression has come from.
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  3. #3
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    Re: Conditional probability question

    Quote Originally Posted by mr fantastic View Post
    \frac{\frac{1}{3} \times \frac{1}{6}}{\frac{1}{3} \times \frac{1}{6} + \frac{1}{3} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{4}} = ....

    Your job is to review conditional probability so that you understand where this expression has come from.
    I understand where this expression has come from, however you have missed the part where it says the salesman visited 2 of the 3 cities.
    Your answer is correct for the case the salesman has visited only 1 of the 3 cities (2/9).
    The answer to my question should be 0.621.
    My problem is that I don't how to reach it.

    (Sorry for my English)
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