Question

An urn contains 9 black and 8 pink balls. Five balls are randomly drawn from the urn in succession, with replacement. Thatis, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn areblack? Round your answer to three decimal places.

Answer 1

There are 9 + 8 = 17 balls in the urn each time (since after each draw the ball is returned), therefore the probability of drawing a black ball each time is:

Probability = number of black balls/total number of balls

Probability = 9/17

Therefore, the probability of drawing a black ball each time is 9/17. In order to find the probability of drawing a black ball 5 times, we just have to raise the probability we found to 5, then we get:

Probability = (9/17)^5 = 0.041

Then, the probability that all 5 balls drawn from the urn are

black is 0.041