Chapter SixDay One

Probability SimulationThe Study of Randomness

P. 397 1-5 all P. 402 7-12 all

Homework

Try to estimate the likelihood of a result of interest by actually observing the random phenomenon many times and calculating the relative frequency of the results – time consuming and expensive

Develop a probability model and use it to calculate a theoretical answer.

Start with a model and simulate a number of repetitions of the procedure.

How to Calculate Likelihood of an Event

If there are 100 seats on an airplane, but the airline books 105 customers knowing that on average five percent of customers do not show, how often will the flight be overbooked?

If you flip a coin ten times what is the probability of getting at least one run of 3 or more consecutive tails or heads?

Examples

Example Use simulation to estimate the probability of getting

three or more consecutive heads or tails in ten tosses of a fair coin.

State problem:

State assumptions:

Assign digits:

Simulate many repetitions:

State conclusions:

State Problem: A couple plans to have children until they have a girl or until they have four children whichever comes first. Estimate the probability that they will have a girl.

State assumptions:

Assign digits:

Simulate many repetitions:

State Conclusions:

Example

P. 401 example 6.8

Sevtlana Khorkina earned a 38. 211 in Athens.

Carly Petterson

Mean Standard Deviation Vault 9.314 .216 Parallel 9.553 . 122 Balance 9.461 .203 Floor 9.543 .099

Example