A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

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The probability that none of the balls drawn is blue can be approached in many ways. I will show you two ways you can solve this problem.

Method 1

Let be a random variable representing “picking a blue ball” in a random pick from 2 red, 3 green, and 2 blue balls. Then, using binomial distribution, . The probability that is equal to a value is given by .

Here, there are two draws of a ball, so . Thus, the probability that none of the balls drawn is blue (), is given by

.

Method 2

The probability that ‘the first’ ball is not blue is 1 minus the probability of blue = .

The probability that ‘the second’ ball is not blue is 1 minus the probability of blue = .

The probability that ‘the first’ ball is not blue AND ‘the second’ ball is not blue = .