Question

Five identical bowls are labeled 1, 2, 3, 4, and 5. bowl i contains i white and 5 − i black balls, with i = 1, 2, . . . , 5. a bowl is randomly selected and two balls are randomly selected (without replacement) from the contents of the bowl. a what is the probability that both balls selected are white? b given that both balls selected are white, what is the probability that bowl 3 was selected?

Answer 1

Probability of choosing bowl i = 1/5

Probability that first ball selected is white = i/5

Probability that second ball selected is white = i/4

(a) Probability that both balls selected are white:

           1/5 * i/5 * i/4 = isquared/100

(b) Probability that bowl 3 was selected is 1/5 + isquared/20