An urn contains white and green balls. Four 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 balls drawn from the urn are green? Round your answer to three decimal places.
To find the probability of drawing all green balls, we need to know the number of white balls and green balls in the urn. Let's say there are "W" white balls and "G" green balls in the urn.
Since there are replacement and the balls are returned to the urn after each draw, the probability of drawing a green ball in each draw remains constant. The probability of drawing a green ball in a single draw is calculated as:
P(drawing a green ball) = G / (G + W)
In our case, we're interested in finding the probability of drawing four green balls in succession. Since each draw is independent, we multiply the probability of each event together.
P(drawing all green balls) = P(drawing a green ball in 1st draw) *
P(drawing a green ball in 2nd draw) *
P(drawing a green ball in 3rd draw) *
P(drawing a green ball in 4th draw)
= (G / (G + W)) *
(G / (G + W)) *
(G / (G + W)) *
(G / (G + W))
= G^4 / (G + W)^4
To get the answer, we need to know the number of white balls and green balls in the urn.
Lacking data. How many green and white balls are in the urn?
(green/total)^4 = ?