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Math Help - Probability that both apples are red and at least one maggot

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    [Solved] Probability that both apples are red and at least one maggot

    A box contains 25 apples, of which 20 are red and 5 are green. Of the red apples, 3 contain maggots and of the green apples, 1 contains maggots. Two apples are chosen at random from the box. Find the probability that both apples are red and at least one contains maggot.

    P(Both red and at least one maggot) = P(Red, Red Maggot)+P(Red maggot,Red)+P(Red Maggot,Red Maggot)
    =\frac{20}{25} \times\frac{3}{24}+\frac{3}{25}\times \frac{19}{24}+\frac{3}{25} \times \frac{2}{24}
    =\frac{41}{200}

    but answer is 9/50
    Last edited by Punch; November 23rd 2011 at 10:16 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Probability that both apples are red and at least one maggot

    Quote Originally Posted by Punch View Post
    but answer is 9/50
    Denote R (both red) and M (at least one contains maggots). We have to find p(R\cap M)=p(R)\;p(M|R) .

    p(R)=\dfrac{\displaystyle\binom{20}{2}}{ \displaystyle\binom{25}{2}}=\ldots=\dfrac{19}{30},  \;p(M|R)=1-\dfrac{\displaystyle\binom{17}{2}}{ \displaystyle\binom{20}{2}}=\ldots=\dfrac{25}{95}

    Then, p(R\cap M)=\frac{19}{30}\cdot \frac{27}{95}=\frac{9}{50}
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  3. #3
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    Re: Probability that both apples are red and at least one maggot

    Quote Originally Posted by FernandoRevilla View Post
    Denote R (both red) and M (at least one contains maggots). We have to find p(R\cap M)=p(R)\;p(M|R) .

    p(R)=\dfrac{\displaystyle\binom{20}{2}}{ \displaystyle\binom{25}{2}}=\ldots=\dfrac{19}{30},  \;p(M|R)=1-\dfrac{\displaystyle\binom{17}{2}}{ \displaystyle\binom{20}{2}}=\ldots=\dfrac{25}{95}

    Then, p(R\cap M)=\frac{19}{30}\cdot \frac{27}{95}=\frac{9}{50}
    Thanks! But i dont see anything wrong with my workings too

    Also, could u explain P(M|R) workings?
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  4. #4
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    Re: Probability that both apples are red and at least one maggot

    I figured it out! I included those with maggots when trying to find only red without maggot...
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