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Math Help - tennis ball problem!

  1. #1
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    tennis ball problem!

    A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
    Shift Percentage Percentage
    Produced of Defectives
    1 30% 10%
    2 50% 15%
    3 20% 20%

    If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?
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  2. #2
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    Quote Originally Posted by matty888 View Post
    A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
    Shift Percentage Percentage
    Produced of Defectives
    1 30% 10%
    2 50% 15%
    3 20% 20%

    If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?
    Use Bayes' Rule

    P(S_1 | D) = \frac{P(D | S_1)P(S_1)}{P(D | S_1)P(S_1) + P(D | S_2)P(S_2) + P(D | S_3)P(S_3)}

    P(S_1 | D) = \frac{(0,1)(0,3)}{(0,1)(0,3) + (0,15)(0,5) + (0,2)(0,2)}

    P(S_1 | D) = \frac{6}{29}

    EDIT: Approximately 21%
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  3. #3
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    Quote Originally Posted by matty888 View Post
    A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
    Shift Percentage Percentage
    Produced of Defectives
    1 30% 10%
    2 50% 15%
    3 20% 20%

    If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?
    For a quite similar question (with answer), see http://www.mathhelpforum.com/math-he...tml#post128009.
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  4. #4
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    Quote Originally Posted by janvdl View Post
    Use Bayes' Rule

    P(S_1 | D) = \frac{P(D | S_1)P(S_1)}{P(D | S_1)P(S_1) + P(D | S_2)P(S_2) + P(D | S_3)P(S_3)}

    P(S_1 | D) = \frac{(0,1)(0,3)}{(0,1)(0,3) + (0,15)(0,5) + (0,2)(0,2)}

    P(S_1 | D) = \frac{6}{29}

    EDIT: Approximately 21%
    Ahhhhhhh! And I remember the days when you thought a tree diagram was something you found in a forest .....

    You've come a long way in a short time
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Ahhhhhhh! And I remember the days when you thought a tree diagram was something you found in a forest .....

    You've come a long way in a short time
    Couldn't have done it without the good people of MHF who are always ready to help.

    At the moment I am tackling Binomial Distribution and Random Variables... As soon as I get the hang of one thing, another pops up...
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  6. #6
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    Quote Originally Posted by janvdl View Post
    Couldn't have done it without the good people of MHF who are always ready to help.

    At the moment I am tackling Binomial Distribution and Random Variables... As soon as I get the hang of one thing, another pops up...
    Getting off topic a bit but ...... you've heard of the mythical hydra .....!!

    You might have noticed that there are a lot of quite good binomial distribution questions scattered across the MHF.
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