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What is the Probability of Harry's Selection?

Discussion in 'CAT/MAT/GMAT Preparation' started by Royaluni, Sep 11, 2015.

  1. Royaluni

    Royaluni Administrator

    GMAT Quantitative Practice Question-- A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary and one of the remaining 8 members is to be chosen at random to be the treasure. What is the probability that harry will be either the member chosen to be the secretary or the member chosen to be the treasure?

    A. 1/720

    B. 1/80

    C. 1/10

    D. 1/9

    E. 1/5


    Answer – this is a probability questions and there are two probabilities that we need to calculate in order to answer this question.

    Two probabilities which we need to calculate are;

    1. Whether Harry is selected as Secretary

    Or

    2. Treasure

    Always remember one thing in probability,

    OR Mean Add

    Add Mean Multiply

    So in this question we will first calculate the individual probabilities and then add them.

    Probability = Total number desired outcomes/total number of possible outcomes

    Probability questions always deals with various scenarios for a given case. In this question, in order to satisfy our required conditions, there are two scenarios;

    1. Harry cannot be selected as President if Harry is to be Secretary because one person can only be selected for one job.

    2. Harry cannot be selected for both, President and Secretary if he is to be selected for treasure.

    Scenario 1

    Let’s calculate probability of choosing Harry for Secretary;

    As mentioned earlier, he cannot be chosen for president job if he need to selected for Secretary, so we first need to calculate the probability of Harry for President’s Job;

    Total member of the group = 10

    Desired outcome = 1

    Probability of Harry for President = 1/10

    Now calculate the probability of Harry not chosen for President because then only he will qualify for Secretary Job. In order to do that, we subtract probability of Harry for president from total probability;

    Probability of Harry Not Being Chosen for President= 1 – 1/10= 9/10

    Now if harry is selected as Secretary, he won’t be chosen for Treasure, so probability of Harry of being Treasure will be 0;

    1-0=1

    Finally, probability of Harry chosen for Secretary = 9/10 * 1/9 * 1 = 1/10

    Scenario 2

    As mentioned earlier, Harry can only qualify for Treasure’s job if he is neither chosen for President’s nor Secretary’s job.

    We have already calculated in scenario 1 that,

    Probability of Harry Not Being Chosen for President= 1 – 1/10= 9/10

    Probability of Harry Not Being Chosen for Secretary = 1- 1/9 = 8/9

    Probability of Harry Being Chosen for Treasure = 1/8

    So total probability for Treasure = 9/10 * 8/9 * 1/8 = 1/10

    Now question is asking the probability of Harry being chosen as Secretary or Treasure, so we will add them to find out the total probability;

    1/10 + 1/10 = 2/10 = 1/5 , answer choice E

    Source- Official GMAT 2016 Guide

    How many of the 200 households surveyed used both brands of soap?
     
    Last edited: Sep 11, 2015

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