Question

An urn contains 8 red and 6 green 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 green? round your answer to three decimal places.

Answer 1

The probability of drawing 5 green balls in succession from the urn with replacement is 0.040.

Step-by-step explanation:

To calculate the probability of drawing 5 green balls with replacement, we need to calculate the probability of drawing 1 green ball in each of the 5 draws. Since each draw is independent, the probability for each draw remains the same. The probability of drawing a green ball is 6/14, or 0.429 rounded to three decimal places. Therefore, the probability of drawing 5 green balls in succession is (0.429)^5 = 0.040 rounded to three decimal places.

Answer 2

8 red, 6 green......14 total

P(green) = 6/14 which reduces to 3/7
replaced
if the ball is being replaced each time, the sample size does not change

therefore, the probability of all 5 balls being green is (3/7)^5 = 3^5/7^5 =
243/16807 = 0.014 <==