probability distribution?

In a large bag of marbles, 20% are red. You choose 4 marbles from this bag. If you choose the marbles at random, what is the chance that you get exactly 3 red marbles?

In a large bag of marbles, 20% are red. You choose 4 marbles from this bag. If you choose the marbles at random, what is the chance that you get exactly 3 red marbles?

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Since the bag is "large," we do not need to worry about changing the odds once we have removed a marble.

Suppose you drew 3 red, followed by a non-red. The probability would be

P(RRRnr) = (.2)(.2)(.2)(1 - .2) = .0064

However, the “non-red” marble could be chosen first, second, or third also, so there are four different arrangements that meet the criteria:

RRRnr
RRnrR
RnrRR
nrRRR

The probability is the same (.0064) for each case, and the probability of getting 3 red in 4 draws is the sum of these individual probabilities:

P( 3 red out of 4) = 4(.0064) = .0256

Make sense?