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Math Help - Conditional Probability: Company's Acceptance Rates

  1. #1
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    Conditional Probability: Company's Acceptance Rates

    Hello everyone,

    After solving the following question on conditional probability, I had doubts about the answer given by my textbook which I've posted in white below.

    Therefore, could anyone please check my final answer and work shown below?

    Thank you very much.

    ---

    Question: Making Money Corporation is hiring and has two stages in its application process. The first part is a written test on finance and the second is an interview. Making Money Corporation uses the written test to screen out applicants, so that not all applicants are given an interview. But all those who are successful must be interviewed. If Making Money Corporation accepts 10% of all applicants, and 20% of all applicants are given an interview, what is the probability that an interviewed candidate will be accepted? Assume that all those who are offered an interview attend.

    My Solution: Let G = the probability of getting an interview, and A = the probability that an applicant will be accepted.

    Then  P(A | G) = \cfrac{P(A \cap G)}{P(G)}

    Know:  P(A) = 0.10, P(G) = 0.20. Since all those who accepted were interviewed, P(A \cap G) = 0.10.

     \Rightarrow P(A | G) = \cfrac{0.10}{0.20} = 0.50 .

    Textbook's Solution (hidden in white): 0.83
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  2. #2
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    Quote Originally Posted by scherz0 View Post
    Hello everyone,

    After solving the following question on conditional probability, I had doubts about the answer given by my textbook which I've posted in white below.

    Therefore, could anyone please check my final answer and work shown below?

    Thank you very much.

    ---

    Question: Making Money Corporation is hiring and has two stages in its application process. The first part is a written test on finance and the second is an interview. Making Money Corporation uses the written test to screen out applicants, so that not all applicants are given an interview. But all those who are successful must be interviewed. If Making Money Corporation accepts 10% of all applicants, and 20% of all applicants are given an interview, what is the probability that an interviewed candidate will be accepted? Assume that all those who are offered an interview attend.

    My Solution: Let G = the probability of getting an interview, and A = the probability that an applicant will be accepted.

    Then  P(A | G) = \cfrac{P(A \cap G)}{P(G)}

    Know:  P(A) = 0.10, P(G) = 0.20. Since all those who accepted were interviewed, P(A \cap G) = 0.10.

     \Rightarrow P(A | G) = \cfrac{0.10}{0.20} = 0.50 .

    Textbook's Solution (hidden in white): 0.83
    My interpretation of the question leads to 1/2 as well.
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