Probability

There are 120 students in a class of boys and girls. One student is to be chosen to represent the class and each student is equally likely to be chosen. If the probability that the student chosen is a boy is \frac{2}{3} of the probability that the student chosen is a girl, find the number of girls in the class.

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5 thoughts on “Probability”

  1. well, to start of, we cannot say directly that the ratio for boy is 2, and the ratio for girl is 3. It is somewhat correct, but it is not proven before performing any set of calculation.

    So, let the probability for girl is x. And “student chosen is a boy is 2/3 of the probability that the student chosen is a girl”, thus probability is 2/3*x.

    We know that the sample space will be 120, as there is 120 students. We know that the sum of the probabilities of the distinct outcomes within the sample space is equal to 1.

    so using an simple algebra equation, we can say that:
    x+2/3 x=1
    3/3 x+2/3 x=1
    5/3 x =1
    x= 3/5

    So, the probability for the girls is 3/5.

    P(girls) = n(girls) / n(sample space).
    3/5 = n(girls)/120
    n(girls) = 3/5*120
    n(girls) = 72 students.

  2. Ratio (boy) = 2
    Ratio (girl) = 3
    Total ratio = Ratio (boy+girl) = 2+3 = 5

    Total = 120 students
    Boy = 2/5 * 120 = 48 students –> ratio (boy) / total ratio * total students
    Girl = 3/5 * 120 = 72 students –> ratio (girl) / total ratio * total students

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