Question

A box contains 4 white balls and 5 red balls. I draw 3 of them out of the box, one at a time, without replacement. What is the probability that the balls I draw alternate between the two colors?

Answer 1

Let A be the probability of drawing a white ball first, then a red one second, and then a white one last.

Let B be the probability of drawing a red ball first, then a white one second, and then a red one last.

So, P(A or B) =

[4/9 x 5/8 x 3/7 = 60/504 ] + [ 5/9 x 4/8 x 4/7 = 80/504 ] =

[60 + 80 ] / 504 = 140/504 = 5/18 = about 27.8%