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Balls White

Balls White

Roll a dice and pick a ball - Probability of all balls being white is?

A bag contains 6 white and 4 black balls. A fair dice is rolled and number of balls equal to the number rolled by the dice are randomly picked from the bag. What is the probability that all the balls selected are white?

Probability of die showing a 1 and picking 1 white ball:
(1/6)(6/10) = 1/10

Probability of die showing a 2 and picking 2 white balls:
(1/6)(6/10)(5/9) = 1/18

Probability of die showing a 3 and picking 3 white balls:
(1/6)(6/10)(5/9)(4/8) = 1/36

Probability of die showing a 4 and picking 4 white balls:
(1/6)(6/10)(5/9)(4/8)(3/7) = 1/84

Probability of die showing a 5 and picking 5 white balls:
(1/6)(6/10)(5/9)(4/8)(3/7)(2/6) = 1/252

Probability of die showing a 6 and picking 6 white balls:
(1/6)(6/10)(5/9)(4/8)(3/7)(2/6)(1/5) = 1/1260

Add up all the probabilities to get 0.20, or 20%.

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