A bin has 8 black balls and 7 white balls. 3 of the balls are drawn at random. What is the probability of drawing 2 of one color and 1 of the other color?

RektTheNoob
Sep 26, 2017

#1**+1 **

Number of ways to draw 2 black and 1 white = C( 8,2) * C(7,1) (1)

Number of ways to draw 1 black and 2 white = C( 8,1) * C(7,2) (2)

Number of ways to draw 3 balls from 15 = C( 15,3) (3)

Total Probability = [ (1) + (2) ] / (3) =

[ C( 8,2) * C(7,1) + C( 8,1) * C(7,2) ] / [ C( 15,3) ] = .8 = 80%

CPhill
Sep 26, 2017