Question

There are 100 balls of the same shape and same weight in one bag. The balls' colors are different: 15 red balls, 25 yellow balls, 40 blue balls and 20 white balls. You are blindfolded and asked to draw three balls from the bag without replacement. Calculate the probability that there is exactly one white ball among the three balls.

Answer 1

Total number of balls = 100

Number of red balls = 15

Number of yellow balls= 25

Number of blue balls = 40

Number of white balls = 20

Total possible ways such that 3 balls can be drawn from the bag = 100C3 = 161700

Number of ways of selecting 1 white ball from all 20 white balls = 20C1 = 20

Excluding white balls there is 100 - 20 = 80 remaining balls (15 red balls, 25 yellow balls, 40 blue balls)

Number of ways of selecting 2 balls from remaining 80 balls = 80C2 = 3160

All possible ways of drawing exactly one white ball among the three balls = (Number of ways of selecting 1 white ball from all 20 white balls Number of ways of selecting 2 balls from remaining 80 balls)

All possible ways of drawing exactly one white ball among the three balls = 20 3160 = 63200

probability that there is exactly one white ball among the three balls= (All possible ways of drawing exactly one white ball among the three balls Total possible ways such that 3 balls can be drawn from the bag )

probability that there is exactly one white ball among the three balls= (63200 161700) = 0.3908

Answer: The probability that there is exactly one white ball among the three balls is 0.3908