A box contains 4 white b***s and 5 red b***s. I draw 3 of them out of the box, one at a time, without replacement. What is the probability that the b***s I draw alternate between the two colors?
+130517 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%
+130517 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%
