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.
What is the relationship between the number of white and red balls?
To find the probability that all balls drawn from the urn are white, we need to calculate the probability of drawing a white ball on each individual draw and multiply them together.
Let's assume that the urn contains n total balls, out of which w are white and r are red.
Since we are drawing with replacement, the probability of drawing a white ball on each draw remains the same for all draws.
Thus, the probability of drawing a white ball on any individual draw is w/n.
Since we are drawing four balls in succession, the probability of drawing four white balls is (w/n) * (w/n) * (w/n) * (w/n) = (w/n)^4.
Now we need to substitute the actual values given in the problem. However, the problem does not mention the number of white and red balls in the urn, so we cannot calculate the exact probability without that information.
If you have the values for n (total number of balls), w (number of white balls), and r (number of red balls), you can substitute those values into the formula (w/n)^4 and calculate the probability.
So, to find the probability, you first need to know the number of white balls, the number of red balls, and the total number of balls in the urn.