Question

An urn contains 5 total balls, which comprise 4 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 exactly 5 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 draw the green ball from an urn on exactly the 5th try is approximately 0.082. This is calculated by multiplying the probability of drawing a white ball four consecutive times (4/5)^4 by the probability of drawing the green ball on the fifth draw (1/5).

Step-by-step explanation:

The question involves calculating the probability that Dwight will draw the green ball from an urn on exactly the 5th try, given that the urn contains 4 white balls and one green ball, and that the ball is replaced each time after drawing. To find this probability, we need to consider that Dwight must draw a white ball in the first four tries and a green ball on the fifth try. Since the draws are independent (the ball is replaced each time), we can multiply the individual probabilities for each draw.

The probability of drawing a white ball is 4/5, and the probability of drawing the green ball is 1/5. Using a TI-83, TI-83 Plus, or TI-84 calculator, we can compute the probability of Dwight drawing the green ball on exactly the 5th try as follows:

1. Calculate the probability of drawing a white ball four times in a row: (4/5)^4.
2. Calculate the probability of drawing the green ball on the fifth draw: 1/5.
3. Multiply the probabilities from steps 1 and 2 together to determine the overall probability.

Thus, the probability is (4/5)^4 * (1/5). When calculated and rounded to three decimal places, the result is approximately 0.082.