A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out...

A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same? color?

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Expert Solution

The box has 2 ?red, 3 white and 3 green balls i.e. a total of 8 balls.

If a red ball is drawn first, the probability thereof is 2/8 or, ¼. Then, there are 7 balls remaining in the box, of which 1 is red so that the probability of drawing a red ball a second time is 1/7. Thus, the probability of drawing 2 red balls is (1/4)*(1/7) = 1/28.

If a white ball is drawn first, the probability thereof is 3/8. Then, there are 7 balls remaining in the box, of which 2 are white so that the probability of drawing a white ball a second time is 2/7. Thus, the probability of drawing 2 white balls is (3/8)*(2/7) = 3/28.

If a green ball is drawn first, the probability thereof is 3/8. Then, there are 7 balls remaining in the box, of which 2 are green so that the probability of drawing a green ball a second time is 2/7. Thus, the probability of drawing 2 green balls is (3/8)*(2/7) = 3/28.

Hence, if 2 balls are drawn out of the box in succession, the probability of drawing 2 balls of the same color is (1/28)+(3/28)+(3/28) = 7/28 = ¼.

milcah answered 1 year ago

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