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Mathematics, 15.04.2020 21:22 RoyalGurl01

Garrett is trying to win a prize from the peel-off label on a restaurant cup. The restaurant claims that 20% of the cups it has in stock have winning labels on them. He wants to know the probability that he will need to purchase at least three cups to win the prize.

Garrett can use one of the following simulations to compute this probability before he spends any money on cups.

Model A - Use a random number generator to generate 500 three-digit numbers from 000 to 999. Assign "success" to the number values of 1 and 2, and count up all the random numbers that have a 1 or 2 in the last digit only or not at all.

Model B - Use a spinner with five different colors of equal area. Assign "success" to one of the colors. For one trial, spin the spinner three times. If the spinner lands on the desired color before the third spin, start over. Count the trial if the spinner either lands on the desired color on the third spin or not at all. Repeat this process for 20 trials.

Model C - Use a standard six-sided die. Assign "success" to the number 1. For one trial, roll the die three times. If the die lands on a 1 before the third roll, start over. Count the trial if the die either lands on a 1 on the third roll or not at all. Repeat this process for 30 trials.

_ is the best simulation for this situation. Using this simulation, the probability that Garrett will need to purchase at least three cups to win the prize is about _ .

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