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Math Help - Simple probability question

  1. #1
    Senior Member Stroodle's Avatar
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    Simple probability question

    Kim goes to the sports centre each evening and either works out in the gym or has a swim. She never has a swim two evenings in a row. If she has a work-out in the gym one evening, then the next evening she is twice as likely to have a swim as she is to have a work-out in the gym. On a particular Monday evening, she works out in the gym.

    What is the probability that she works out in the gym on both the Tuesday and Wednesday evenings of that week?


    I can see that Pr(swim|swim)=0, and that Pr(gym|swim)=1. Just can't get my head around how to get Pr(gym|gym) and Pr(swim|gym).

    Thanks for your help!
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  2. #2
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    Since,"if she has a work-out in the gym one evening, then the next evening she is twice as likely to have a swim as she is to have a work-out in the gym."

    I would say that:

    pr(gym|gym)=1/3

    pr(swim|gym)=2/3

    Since the sum of the two probabilities must equal 1 because it's stated that she does some sort of work out every evening.
    Someone please correct me if I'm wrong.
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  3. #3
    Senior Member Stroodle's Avatar
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    Ahh, of course. That's the same answer as in my text

    Thanks heaps
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