An urn contains 8 black and 9 red 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.

Question

Mathematics

Willie Casey

11 February, 07:10

An urn contains 8 black and 9 red 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.

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Answers (1)

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Katie Oneal · Answer 1

There are 17 balls all together in the urn, and 8 of them are black.

On the first draw, the probability of pulling a black one is 8/17.

Since you return the selected ball to the pot, every draw is like the first one.

Every time, the probability of pulling a black ball is 8/17.

The probability of pulling a black ball five straight times is

(8 / 17) ⁵ = 0.023 (about 2.3%)