Probability of selecting siblings

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LulaBrazilia Really wants to Beat The GMAT! Default Avatar
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Probability of selecting siblings Post Tue Mar 11, 2014 7:00 pm
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    A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

    A) 3/40,000

    B) 1/3,600

    C) 9/2,000

    D) 1/60

    E) 1/16

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    Post Tue Mar 11, 2014 7:07 pm
    LulaBrazilia wrote:
    A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

    A) 3/40,000

    B) 1/3,600

    C) 9/2,000

    D) 1/60

    E) 1/16
    One option is to apply probability rules.

    So, for two siblings to be selected, 2 things must happen: we must select a junior who has a senior sibling AND the senior selected must be the sibling of the selected junior.
    We get P(junior with sibling AND selected senior is sibling to selected junior)= P(junior with sibling) x P(selected senior is sibling to selected junior)

    P(junior with sibling): there are 1000 juniors and 60 of them have senior siblings. So, P(junior with sibling)=60/1000

    P(selected senior is sibling to selected junior): Once the junior has been selected, there is only 1 senior (out of 800 seniors) who is the sibling to the selected junior. So, P(selected senior is sibling to selected junior)= 1/800

    So, the probability is (60/1000)x(1/800) = 3/40,000
    The answer is A

    Cheers,
    Brent

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    Patrick_GMATFix GMAT Instructor
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    Post Tue Mar 11, 2014 7:08 pm
    There are 60/1,000 chances to pick a sibling from the junior class, then only 1/800 chances to pick the matching sibling from the senior class. The probability that both happen is (60/1000)(1/800) = 3/40,000. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).



    -Patrick

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