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    Probability: 3 colors of balls in a bag

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    A basket contains 4 black, 2 blue, and 5 green balls. A sample of 3 balls is drawn. Find the probabilities that the sample, drawn without replacement, contains the following

    All blue balls

    Exactly 2 black balls

    2 green balls and 1 blue ball

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    Solution Preview

    I am going to answer them in a different order, for purposes of explanation.

    All blue balls : Student, this case is easy: zero! Since there are only 2 blue balls, we can never get all blues in a sample of three!

    2 green balls and 1 blue ball : Letting G be a green ball and B be a blue ball, we can do this three ways: BGG, GBG, or GGB. Let's look at each case:

    B on first draw: 2/11 (2 of the 11 in the basket ...

    Solution Summary

    Details on each case and how the probability is calculated.