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urn contains 8 pink and 9 white balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball
returned to the urn. What is the probability that all 6 balls drawn from the urn are white? Round your answer to three decimal places.

Ask by Higgins Nguyen. in the United States
Mar 28,2025

Solución de inteligencia artificial de Upstudy

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The probability that all 6 balls drawn are white is approximately 0.022.

Solución

We are given an urn with 8 pink balls and 9 white balls. The total number of balls is
Since each ball is replaced after being drawn, the draws are independent. The probability of drawing a white ball in one draw is
Since 6 balls are drawn, the probability that all 6 drawn balls are white is
To get a numerical approximation, we compute
Thus, the probability that all 6 balls are white is approximately

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The Deep Dive

To find the probability that all 6 balls drawn from the urn are white, you first need to determine the total number of balls and the probability of drawing a white ball. There are 8 pink balls and 9 white balls, making a total of 17 balls in the urn.
The probability of drawing a white ball on any single draw is the number of white balls divided by the total number of balls:
Since the draws are with replacement, the probability remains the same for each draw. Therefore, the probability of drawing 6 white balls in a row is:
Calculating this gives:
So, rounded to three decimal places, the probability is approximately 0.007.

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