Question

An urn contains 6 red and 8 black balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black? Round your answer to three decimal places.

Answer 1

Since each ball is replaced after it is drawn, the probability of drawing a black ball on any given draw is 8 / (6 + 8) = 4 / 7. The probability of drawing 5 black balls in a row is the product of the probabilities of each individual draw, since the draws are independent of each other. Therefore, the probability of drawing 5 black balls in a row is:

(4/7) * (4/7) * (4/7) * (4/7) * (4/7) = 0.0724

Rounding to three decimal places, the probability that all 5 balls drawn from the urn are black is 0.072.