Simulation
Use a graphing calculator or statistical software to simulate the game of roulette, using an integer distribution for the numbers 1 through 38. Repeat the simulation 100 times. Let the number 37 represent 0 and the number 38 represent 00. Use the results of the simulation to answer the following questions.
b. What is the probability that the ball lands either in the slot marked 0 or in the one marked 00?

Verified step by step guidance

1. Understand that the roulette wheel has 38 slots numbered 1 through 38, where 37 represents 0 and 38 represents 00.
2. Simulate the roulette game 100 times by generating 100 random integers between 1 and 38, each representing the slot where the ball lands.
3. Count the number of times the ball lands in slot 37 (which represents 0) or slot 38 (which represents 00) in your simulation results.
4. Calculate the experimental probability by dividing the count of times the ball landed in 0 or 00 by the total number of simulations (100). Use the formula: \(\text{Probability} = \frac{\text{Number of times ball lands on 0 or 00}}{100}\).
5. Interpret this probability as the estimated chance, based on your simulation, that the ball lands in either the 0 or 00 slot.

Key Concepts

Simulation in Probability

Simulation involves using computational tools to model random processes and approximate probabilities by repeating experiments many times. In this context, simulating roulette spins helps estimate the likelihood of outcomes without relying solely on theoretical calculations.

Discrete Uniform Distribution

A discrete uniform distribution assigns equal probability to each outcome in a finite set. Here, the numbers 1 through 38 represent equally likely slots on the roulette wheel, with 37 and 38 corresponding to 0 and 00, respectively.

Empirical Probability

Empirical probability is calculated from observed data by dividing the number of favorable outcomes by the total number of trials. Using the simulation results, the probability of landing on 0 or 00 is estimated by counting how often these outcomes occur in 100 spins.