Find the probability distribution for  y in the following case: A foreman in a manufacturing plant has three men and three women working for him. He wants to choose two workers for a special job. Not wishing to show any biases in his selection, he decides to select two workers at random. Let y denote the number of women in his selection. Find the probability distribution for y?

Expert Answers

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The foreman in a manufacturing plant has three men and three women working for him. He wants to choose two workers for a special job and picks them at random from the group of 6.

The probability that no women are picked is (3*2)/(6*5)  = 0.2

If one woman is picked she can be either the first or the second, this gives the probability that one woman is picked as (2*3*3)/(6*5) = 0.6

The probability that 2 women are picked is (3*2)/(6*5) = 0.2

The probability distribution for y is 0: 0.2, 1: 0.6 and 2: 0.2

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