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Math Help - Probability

  1. #1
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    Probability

    Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
    What is the probability that you will receive a Merit scholarship?

    What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

    What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
    Please help

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  2. #2
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    P(M \cup A)\quad {\mbox{means at least one}} and P(M \cap A)\quad {\mbox{means both}}.
    You know that P(M \cup A) = P(M) + P(A) - P(M \cap A).
    Now solve for P(M).
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  3. #3
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    Quote Originally Posted by hrunup View Post
    Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
    What is the probability that you will receive a Merit scholarship?

    What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

    What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
    Please help

    Need help
    \Pr(A | M) = \frac{\Pr(A \cap M)}{\Pr(M)}.

    \Pr(M | A) = \frac{\Pr(M \cap A)}{\Pr(A)} = \frac{\Pr(A \cap M)}{\Pr(A)}.
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  4. #4
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    Thanks

    That really clears things up.

    Hrunup
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