There are three boxes Box 1 has one white ball and two black

There are three boxes. Box 1 has one white ball and two black balls. Box 2 has two white balls and one black ball. Box 3 has two white balls and two black balls. You select one ball randomly from each box.In total, three balls are taken from the three boxes. Find the probability that there is exactly one white ball among the three chosen.

Solution

There are three cases here:

1. White, Black, Black
2. Black, White, Black
3. Black, Black, White

where the sequence is in order of the boxes themselves.

Thus,

P(eactly one black) = (1/3)*(1/3)*(2/4) + (2/3)*(2/3)*(2/4) + (2/3)*(1/3)*(2/4)

= 0.388888889 [ANSWER]