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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    A class consists of seven boys and 9 girls. Two different members of the class are chosen at random. A is the event {the first person is a girl}, and B is the event {the second person is a girl}. Find the probability of:

    a) B|A'

    Please Help !
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    Quote Originally Posted by creatively12 View Post
    A class consists of seven boys and 9 girls. Two different members of the class are chosen at random. A is the event {the first person is a girl}, and B is the event {the second person is a girl}. Find the probability of:

    a) B|A'

    Please Help !
    P(B|A) is asking us what if the prob a randomly getting a girl is you have already pick one.

    This just reduces your sample space. After you have picked the first girl there are now 7 boys and 8 girls to choose from.

    To the probability is P(B|A)=\frac{8}{15}

    after thought: does B|A' mean A compliment i.e B|A^c if that is the case the same reasoning as above would still work exept you would remove a boy instead of a girl from your sample space.
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    thnx for the reply, but why u have to take out not from a girl, but from a boy, cause A represents girls, and A' would be 1-A right, so if we say lik, 1-(9/16), then why is it wrong, can you explain this part, i'd really appreciate that
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    Quote Originally Posted by creatively12 View Post
    thnx for the reply, but why u have to take out not from a girl, but from a boy, cause A represents girls, and A' would be 1-A right, so if we say lik, 1-(9/16), then why is it wrong, can you explain this part, i'd really appreciate that
    TES showed you an example of what to do. To paraphrase:

    After you have picked the first boy there are now 6 boys and 9 girls to choose from
    Therefore ....
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  5. #5
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    Hello, creatively12!

    A class consists of 7 boys and 9 girls.
    Two members of the class are chosen at random.
    A = (1st person is a girl}, and B = (2nd person is a girl}.

    Find: . (a)\;P(B\,|\,A')

    We want: . P(B\,|\,A') \;=\;P(\text{2nd is girl}\,|\,\text{1st is a boy})

    Since the first chosen is a boy,
    . . there are 6 boys and 9 girls to choose from.
    Then the probability of choosing a girl is: . \tfrac{9}{15} \:=\:\tfrac{3}{5}

    Therefore: . P(\text{2nd is girl}\,|\,\text{1st is boy}) \;=\;\frac{3}{5}

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