# GMAT Probability: Prob. per Distribution and Equal Likelihoods

## GMAT Probability per Distribution and Equal Likelihoods

A bag contains red and blue balls. Exactly half of the balls are red, and the other half are blue. If four balls are removed from the bag, then replaced, what is the Probability that exactly three blue balls will be among those selected?

First, let’s figure out the number of distributions.

P(B)*P(B)*P(B)*P(R)

Well, it’s four total and three repeated, so by Mississippi we see four total distributions:

4!/3!=4

Next, let’s look at Prob. per distribution, which, given the fact that the balls are replaced, is actually rather straightforward. Remember, it’s a 50% chance of getting either:

P(B)*P(B)*P(B)*P(R)

(1/2)(1/2)(1/2)(1/2)=116

Now all we need to do is multiply the two values we’ve found so far:

number of distributions * prob./distribution=4*(1/16)=3/8

See? Not so bad after all.

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