Question

an urn contains 8 red and 9 green balls. six 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 6 balls drawn from the urn are green? round your answer to three decimal places. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate total number of balls

The urn has 8 red and 9 green balls. So the total number of balls is $8 + 9=17$.

Step2: Calculate probability of drawing a green - ball in one draw

The probability of drawing a green ball in one draw, $P(G)$, is the number of green balls divided by the total number of balls. So $P(G)=\frac{9}{17}$.

Step3: Calculate probability of drawing 6 green balls in a row with replacement

Since the draws are independent (because of replacement), the probability of drawing 6 green balls in a row is $P = (\frac{9}{17})^6$.
$(\frac{9}{17})^6=\frac{9^6}{17^6}=\frac{531441}{24137569}\approx0.022$.

Answer:

$0.022$