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Probability: Different Colours of Marbles

Question: A jar contains 3 white marbles, 2 yellow marbles, 4 red marbles, and 5 blue marbles. Two marbles are picked at random. What is the probability that

a.) Both are blue
b.) Exactly 1 is blue
c.) At least 1 is blue

Solution Preview

(a) The event of choosing 2 marbles has:
14!/(12!2!) = 91 members, corresponding to picking 2 objects out of 14.
The event of choosing 2 blue ones corresponds to choosing 2 blue marbles among 5: 5!/2!3! = 10.
The probability is given by ...

Solution Summary

This solution is comprised of a response of about 175 words which estimates the probability of selecting particular colours of marbles. All calculations which are necessary are illustrated.