AP STATISTICS Section 6.1 Simulations

Objective: To be able to create and carry out a simulation. Probability: the branch of mathematics that describes the pattern of chance outcomes. Models for Estimating Probability 1. Observe and calculate relative frequency. 2. Use a probability model and calculate the theoretical answer. 3. Start with a model and then simulate many repetitions of the procedure.

Simulation is the imitation of chance behavior based on a model that accurately reflects the phenomenon under consideration. Steps: 1. State or describe the problem. 2. State the assumptions. 3. Assign digits to outcomes and describe the procedure. *** 4. Simulate many repetitions. 5. Calculate the relative frequency and state the conclusions. Trial: one repetition of the simulation. Trials are independent if the results of one trial do not influence the results of the next trial.

Ex. 1 Simulate the chance that the Eagles make the playoffs this season.

Ex. 2 Missile Defense Problem. An intercepting missile has a 60% success rate. The government has decided to launch 4 interceptors at each incoming missile. Simulate the likelihood that the incoming missile hits its target. (all interceptors miss)

Ex. 3 The Rumor Problem Ex. 4 The Duck Hunt

Ex. 5 The Birthday Problem Ex. 6 The Baseball Problem