math

Three cards are drawn at random without replacement from a standard deck of 52 playing cards. What is the probability that the second and third cards are black?

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  1. There were 52 cards. Half were black
    so
    26/52 = .5
    then we had 51 cards, 25 black
    25/51
    then we had 50 cards, 24 black
    24/50
    so
    .5 * 25/51 * 24/50

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    Damon
  2. Did not say that the first card could have been black also, so ..
    26 Black , 26 Red

    case 1, the first card was also black, that is, BBB
    prob of that = (26/52)(25/51)(24/50)

    case 2, the first card was not black, but the other two were black, that is, RBB
    prob of that = (26/52)(26/51)(25/50)
    prob of your event = (26/52)(25/51)(24/50) + (26/52)(26/51)(25/50)
    = (26/52)((25/51)(24/50) + (26/51)(25/50)
    = (26/52)(25*24 + 26*25)/(50(51))
    = ....

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    Reiny
  3. Oh, thanks, did not notice that.

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    Damon

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