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Manhattan GMAT

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bryan88 Really wants to Beat The GMAT! Default Avatar
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Manhattan GMAT Post Sun May 06, 2012 11:03 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?

    A) 24/91
    B) 45/91
    C) 2/3
    D) 67/91
    E) 84/91

    What is the 1-x method to this?

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    aneesh.kg GMAT Destroyer!
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    Post Sun May 06, 2012 11:25 am
    A team of 12 has to be selected from a pool of 10 men and 5 women.

    The 1-x method:
    The only unfavourable case is when in the team of 12, we have 7 Men and 5 Women.
    So, we will subtract the probability of that from 1.

    The required probability is:
    1 - [P(7M,5W)]
    = 1 - [10C7*5C5/15C12]
    = 1 - (120/455)
    = 335/455
    = 67/91 (Option D)

    Alternatively:
    We will add up the probability of all the favourable outcomes.

    The required probability is:
    P(8M,4W) + P(9M,3W) + P(10M, 2W)
    = 10C8*5C4 / 15C12 + 10C9*5C3 / 15C12 + 10C10*5C2 / 15C12
    = (45*5 + 10*10 + 1*10)/(5*7*13)
    = 67/91 (Option D)

    Same Answer.

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    bryan88 Really wants to Beat The GMAT! Default Avatar
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    Post Sun May 06, 2012 11:40 am
    A case of 6 men and 6 women wont exists as the number of women is capped at 5.
    Tricky question under time constraints.

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    Anurag@Gurome GMAT Instructor
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    Post Sun May 06, 2012 8:55 pm
    bryan88 wrote:
    If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?

    A) 24/91
    B) 45/91
    C) 2/3
    D) 67/91
    E) 84/91

    What is the 1-x method to this?
    The following combinations are possible: (8M, 4W), (9M, 3W), (10M, 2W)
    Total number of ways of selecting a jury of 12 people from 15 people = 15C12 = (15 * 14 * 13)/3 * 2) = 5 * 7 * 13
    Required Probability = (10C8 * 5C4) + (10C9 * 5C3) + (10C10 * 5C2)/(5 * 7 * 13)
    = [(5 * 9 * 5) + (10 * 5 * 2) + (5 * 2)]/(5 * 7 * 13)
    = [(9 * 5) + (10 * 2) + 2]/(7 * 13)
    = 67/91

    The correct answer is D.

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