Question

A roulette wheel has 38 slots, numbered 1 to 36, with two additional green slots labeled 0 and 00. Jim, a dealer at a roulette table, tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands. The ball has an equally likely chance of landing in each slot. If Jim spins the ball around the wheel 20 times, what is the probability that the ball lands in a green slot at most once? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.

Round your answer to three decimal places.

Answer 1

The probability that the ball lands in a green slot at most once in 20 spins is approximately 0.891.

Step-by-step explanation:

To find the probability that the ball lands in a green slot at most once in 20 spins, we need to calculate the probability of landing in a green slot 0 or 1 times.

First, we can calculate the probability of landing in a green slot 0 times. The probability of not landing in a green slot in one spin is 36/38, so the probability of not landing in a green slot in 20 spins is (36/38)^20.

Next, we can calculate the probability of landing in a green slot exactly once. The probability of landing in a green slot in one spin is 2/38, so the probability of landing in a green slot once in 20 spins is (2/38) * (36/38)^19 * C(20,1), where C(20,1) represents the number of ways to choose 1 spin out of 20.

Finally, we add these two probabilities together to get the probability of landing in a green slot at most once. Using a TI-83, TI-83 Plus, or TI-84 calculator, we can calculate this probability to be approximately 0.891.