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Math

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Need help on how to solve this problem..
Five cards are chosen from a deck of playing cards and put into a pile. Three of the cards are red and 2 of the cards are black. A second pile is made using 2 red cards and b black cards. One card from each pile is chosen randomly. The probability of choosing a red card from each of the piles is 6/45. How many black cards, b , are in the second pile? The answer is 7 but I don't know why that is the answer. Thanks...

  • Math -

    call the 2 piles x and y
    P(x) = 3/5
    P(y) = 2/(b+2)

    3/5 * 2/(b+2) = 6/45
    6 / 5(b+2) = 6/45
    5(b+2) = 45
    b+2 = 9
    b = 7

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