Question

An urn contains five black balls and six white balls. Four balls are randomly drawn from the urn in succession with replacement. What is the probability that all four balls drawn from the urn are black? Round your answer to three decimal places.

Answer 1

The probability of drawing four black balls in succession with replacement from an urn containing five black balls and six white balls is approximately 0.043.

Step-by-step explanation:

The probability that all four balls drawn from the urn are black can be calculated by using the rules of probability for independent events with replacement.

Since the balls are drawn with replacement, the probability of drawing a black ball remains constant on each draw.

There are 5 black balls out of a total of 11 balls, so the probability of drawing a black ball in one draw is 5/11.

Since each draw is independent, the probability of drawing four black balls in succession is:

(5/11) × (5/11) × (5/11) × (5/11) = 625/14641 ≈ 0.043

We round this to three decimal places to get 0.043 as the final answer.