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Thread: Probability

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    Probability

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    From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

    a) 3/7
    b) 5/12
    c) 27/70
    d)2/7
    e) 9/35

    Answer : c) 2/7

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    Re: Probability

    Answer: 4 people can be selected out of 8 people in 8C4 ways = 70 (total number of cases). Assuming that Andrew is among the 4 volunteers selected, we have 3 remaining spots for 6 candidates (as Karen can't be on the same team as Andrew we do not consider her as a candidate for the first team). Now, 3 people can be selected out of 6 candidates in 6C3 ways = 20 (favorable number of cases). Our required probability P = Favorable Number of Cases / Total Number of Cases = 20/70 = 2/7.

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    Re: Probability

    Quote Originally Posted by shiladitya View Post
    From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

    a) 3/7
    b) 5/12
    c) 27/70
    d)2/7
    e) 9/35
    P(Andrew is selected but Karen is not selected) = (number of 4-person groups with Andrew but not Karen)/(total # of 4-person groups possible)

    number of 4-person groups with Andrew but not Karen
    Take the task of creating groups and break it into stages.

    Stage 1: Place Andrew in the 4-person group
    We can complete this stage in 1 way

    Stage 2: Send Karen out of the room and, from the remaining 6 volunteers, select 3 more people.
    Since the order in which we select the 3 volunteers does not matter, we can use combinations.
    We can select 3 people from 6 volunteers in 6C3 ways (20 ways).

    By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 4-person group) in (1)(20) ways (= 20 ways)

    total # of 4-person groups possible
    We can select 4 people from all 8 volunteers in 8C4 ways ( = 70 ways).

    So, P(Andrew is selected but Karen is not selected) = (20)/(70) = 2/7

    Cheers,
    Brent - GMAT Prep Now

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