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Math Help - Conditional probability

  1. #1
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    Conditional probability

    10. The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and, in 35 families, the son attended college while the father did not.

    a. What is the probability a son attended college given that his father attended college? 0.22 (3 pts)

    b. What is the probability a son attended college given that his father did not attend college? 0.35 (3 pts)


    My answers are wrong and I followed the joint probability formula..
    Last edited by mr fantastic; November 11th 2009 at 06:11 PM. Reason: Changed post title.
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  2. #2
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    Quote Originally Posted by desire150 View Post
    10. The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and, in 35 families, the son attended college while the father did not.

    a. What is the probability a son attended college given that his father attended college? 0.22 (3 pts)

    b. What is the probability a son attended college given that his father did not attend college? 0.35 (3 pts)


    My answers are wrong and I followed the joint probability formula..
    a. Write F if the father attended college and S if the son attended college.

    By the definition of conditional probability,
    P(S | F) = \frac{P(F \text{ and } S)}{P(F)} = \frac{0.22}{0.22 + 0.12}
    which is approximately 0.647.
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  3. #3
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    Conditional Probability

    Thank you very much for helping me out. I will use the formula provided to finish the question.

    thank you again.
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  4. #4
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    Using the formula provided, here is the answer I came up with. Please let me kow if this is correct or incorrect?
    What is the probability a son attended college given that his father did not attend college

    0.614
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  5. #5
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    Hello, desire150!

    The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons:
    in 22 families, both father and son attended college.
    in 31 families, neither father nor son attended college.
    in 12 families, the father attended college while the son did not.
    in 35 families, the son attended college while the father did not.

    (a) What is the probability a son attended college, given that his father attended college?

    (b) What is the probability a son attended college, given that his father did not attend college?

    Tabulate the facts and their probabilities.

    . . \begin{array}{c||c||ccc}<br />
& \text{College} &  & \\ \hline\hline<br />
\text{Father \& son} & 22 & P(F \wedge S) &=& 0.22 \\ <br /> <br />
\text{Father only} & 12 & P(F \wedge \sim\!S) &=& 0.12 \\ <br /> <br />
\text{Son only} & 35 & P(\sim\!F \wedge S) &=& 0.35 \\ <br /> <br />
\text{Neither} & 31 & P(\sim\!F \wedge \sim\!S) &=& 0.31 \\ \hline \end{array}


    Now you can use Bayes' Theorem to answer the questions.

    . . \begin{array}{cccc}(a) &P(S\,|\,F) &=& \dfrac{P(S \wedge F)}{P(F)} \\ \\[-3mm]<br /> <br />
(b) & P(S\,|\,\sim\!F) &=& \dfrac{P(S \wedge \sim\!F)}{P(\sim\!F)} \end{array}

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  6. #6
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    Thank you so much for the response. Here are my answerws using the formulas

    a) .22
    _________
    .22+.12 =0.647

    b)
    .35
    _____
    .35+.31 = 0.530

    Thank you. I'm finally getting his now..
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