statistics

A bag contains 7 red marbles, 6 white marbles, and 10 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?

What is the probability that exactly two of the marbles are red?

What is the probability that none of the marbles are red?

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  1. prob(probability that all the marbles are red)
    = (7/23)(6/22)(5/21)(4/20) = 1/253

    or, by combinations:
    prob(all 4 red) = C(7,4) / C(23,4) = 35/8855 = 1/253

    b) probability that exactly two of the marbles are red
    = C(7,2)*C(16,2) / C(23,4) = 21*120/8855 = 72/253

    c) probability that none of the marbles are red ---> implies they are either white or blue
    = C(16,4) / C(23,4) = ...

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