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Can you answer this probability question?

  • A gumball machine contains 4 red gumballs and 7 white gumballs. Two gumballs are purchased, one after the other, without replacement. Find the probability that at least one gumball is white.


  • 7/13, because there is a total of 13 gumballs


  • Let's instead figure the probability they are both red:

    On the first purchase you have a 4/11 chance of getting a red ball. Now the machine has 3 red and 7 white.

    On the second purcahse you have a 3/10 chance of getting a red ball.

    Combining the two probabilities, the chance you get two red balls is:
    4/11 x 3/10 = 12/110 = 6/55

    And if you *don't* get two reds, then you must have gotten at least one white. Subtract from 1:

    1 - 6/55
    = 55/55 - 6/55
    = 49/55

    Answer:
    49/55 (approx. 89.1%)







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