Suppose you have a bag of marbles with 3 yellow marbles, 2 blue marbles, 6 red m

Question

Suppose you have a bag of marbles with 3 yellow marbles, 2 blue marbles, 6 red marbles, and 4 green marbles. Answer your question in the form of a fraction. For example, if there is a 50% chance of something happening, type 1/2 for your answer. Three marbles are drawn with replacement. The chance of drawing all red marbles is Three marbles are drawn with replacement. The chance of none of the marbles are red Three marbles are drawn with replacement. The chance the at least one of the marbles was red

Explanation / Answer

There are 3 yellow, 2 blue, 6 red and 4 green marbles.

Three red marbles can be chosen out of six in 6C3 ways. Probability that all three are red marbles = 6C3 / 15C3 = 20 / 455 = 0.0440.

Three non-red marbles can be chosen out of nine in 9C3 ways. Probability that none of the three are red marbles = 9C3 / 15C3 = 84 / 455 = 0.1846.

The probability that atleast one of the marbles is red = 1 - 0.1846 = 0.8154.

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