Question

An urn contains 40 total balls, which comprise 39 white balls and one green ball. Dwight is running an experiment where he draws a ball from the urn, records the color, and replaces the ball, repeating until he draws the green ball. What is the probability that Dwight will take at most 10 tries to draw the green ball from the urn? Use a TI-83, TI-83 Plus, or TI-84 calculator to find the probability, rounding to three decimal places.

Answer 1

The probability that Dwight will take at most 10 tries to draw the green ball from the urn is approximately (0.974).

Step-by-step explanation:

To find the probability, we can use the complement rule. The probability of drawing the green ball in the first 10 tries is equal to 1 minus the probability of not drawing the green ball in the first 10 tries. The probability of not drawing the green ball in a single draw is the ratio of the number of non-green balls to the total number of balls, which is
`\( (39)/(40) \).`

Therefore, the probability of not drawing the green ball in the first 10 tries is
`\( \left((39)/(40)\right)^(10) \).` Using the complement rule, the probability of drawing the green ball in the first 10 tries is
`\( 1 - \left((39)/(40)\right)^(10) \).` Calculating this expression gives us approximately (0.974), rounded to three decimal places.