An urn contains white and red 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 white? Round your answer to three decimal places.
To find the probability that all four balls drawn from the urn are white, we need to know the total number of balls and the number of white balls in the urn.
Let's assume the urn contains n total balls, with w of them being white. In this case, we have n choices for the first ball draw, and since we are replacing the balls after each draw, we still have n choices for the second, third, and fourth draws as well.
The probability of drawing a white ball on each draw is given by:
P(white ball on a single draw) = Number of white balls / Total number of balls
For the first draw, the probability of drawing a white ball is w/n.
Since we are replacing the balls after each draw, the probability of drawing a white ball on each of the four draws is (w/n) * (w/n) * (w/n) * (w/n).
To find the probability that all four balls drawn are white, we multiply the probabilities of each individual draw together:
P(all white balls) = (w/n)^4
Now, we need to round the answer to three decimal places.
Please provide the total number of balls in the urn and the number of white balls so that we can calculate the probability.