SOLUTION: A box contains 2 red and 3 blue marbles. Find the probability that if two marbles are drawn at random (without replacement), (a) both are blue, (b) both are red, (c) one is red and

Question 1176730: A box contains 2 red and 3 blue marbles. Find the probability that if two marbles are drawn at random (without replacement), (a) both are blue, (b) both are red, (c) one is red and one is blue.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Mathematically, there is no difference between drawing the marbles at the same time or one after the other. So calculate the probabilities using the probability that each draw gets the desired outcome. For example,

(a) both blue: the first draw must be blue (3 of the 5 are blue), and the second must also be blue (2 of the remaining 4 are blue). So

P(blue,blue) = (3/5)(2/4)

(b) both red: calculate the probability the same way as for both blue, of course using the appropriate fractions.

(c) one red and one blue: Calculate this again in the same way; but note that the draws can be red then blue or blue then red. So the answer for this case requires adding the results of two such calculations.

Finally, note that the three cases (both blue, both red, or one of each) are the only possible outcomes, so the sum of the probabilities for the three cases must be 1. That will give you a chance to see if you have done the calculations correctly.

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