What is the probability that at least 6 of the balls are white?

Question

An urn has 15 balls that are identical except that 7 are white and 8 are red. A sample of 8 is selected randomly without replacement.

Answer 1

We need to determine the probability of selecting each colored ball.

P(White) = 7/15 = 0.47

P(Red) = 8/15 = 0.53

Use the binomial coefficient to see how many different ways to select at least 6 red balls. Then we will determine the probability from there.

P(X ≥ 6) = [8!/(6!)(2!)]*(0.47)⁶(0.53)² + [8!/(7!)(1!)]*(0.47)⁷(0.53)¹ + [8!/(8!)(0!)]*(0.47)⁸(0.53)⁰

= 28(0.47)⁶(0.53)² + 8(0.47)⁷(0.53) + 1(0.47)⁸

= 0.0848 + 0.0215 + 0.00238 = 0.10868

The probability of selecting at least 6 white balls out of the 8 is 0.10868.