Using Technology to Conduct a Simulation

Warm Up There is a 30% chance that T’Shana’s county will have a drought during any given year. She performs a simulation to find the experimental probability of a drought in at least 1 of the next 4 years.

A simulation is useful in modeling experimental probabilities when an actual trial is too difficult, time-consuming, or costly to perform. A simulation is designed so that its outcomes reflect ways that outcomes occur in the real world. Each possible outcome must be linked to one or more random numbers. Coins, number cubes, spinners, random number tables, and random number generators can be used to generate random numbers for a simulation. Note that as more trials of the simulation are performed, the experimental probabilities will more closely approximate the theoretical probabilities associated with the experiment.

In a survey of 100 male and 100 female students, 52% of females and 38% of males responded that they exercise at least 3 times per week. Find the theoretical probability that a randomly selected student from the survey group exercises at least 3 times per week.

Every contestant on a game show has a 40% chance of winning Every contestant on a game show has a 40% chance of winning. In the simulation below, the numbers 1–4 represent a winner, and the numbers 5–10 represent a nonwinner. Numbers were generated until one that represented a winner was produced.

Over a 100-year period, the probability that a hurricane struck Rob’s city in any given year was 20%. Rob performed a simulation to find an experimental probability that a hurricane would strike the city in at least 4 of the next 10 years. In Rob’s simulation, 1 represents a year with a hurricane.