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Math Help - Help please- Probability question

  1. #1
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    Help please- Probability question

    I am trying to help my cousin and I am unable to get the answer that is given by the book:

    Question is:

    A survey is carried out on a group of 100 students, 60 of whom are boys.

    Find the probability that any 2 students chosen at random from the original group will be both girls.

    thanks
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  2. #2
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    Hello, dominion!

    A survey is carried out on a group of 100 students, 60 of whom are boys.

    Find the probability that any 2 students chosen at random from the original group will be both girls.
    I assume that the choosing is done without replacement.

    There are: 60 boys and 40 girls.


    Method #1

    There are: . {100\choose2} \:=\:4950 possible pairs of students.

    To choose 2 girls, there are: . {40\choose2} \:=\:780 ways.

    Therefore: . P(\text{noth girls}) \;=\;\frac{780}{4950} \;=\;\frac{26}{165}



    Method #2

    The probability that the first student is a girl is: . \frac{40}{100}
    The probability that the second student is a girl is: . \frac{39}{99}

    Therefore: . P(\text{both girls}) \;=\;\frac{40}{100}\cdot\frac{39}{99} \;=\;\frac{26}{165}

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