Define simulation

The imitation of chance behavior, based on a model that accurately reflects the phenomenon under consideration.

List the five steps involved in a simulation

1) State the problem or describe the random phenomenon

2) State the assumptions

3) Assign digits to represent outcomes

4) Simulate many repetitions

5) State your conclusions

Explain what is meant by independent trials

The results of one outcome have no effect or influence over the next outcome. All the outcomes have the same possible outcomes and probabilities.

Use a table of random digits to carry out a simulation

Digits: 19223 95034 05756 28713 96409 12531

H/T: HHTTH HHTHT THHHT TTHHH HTTTH HTHHH

Given a probability problem, conduct a simulation in order to estimate the probability desired.

34893 43898 30920 10573

HHTTH HTHTH HHHTT TTTTH

Use a calculator or a computer to conduct a simulation of a probability problem

(See computer)

6.2 Objectives

Explain how the behavior of a chance event differs in the short- and long-run

Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.

Explain what is meant to be a random phenomenon

If individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.

Explain what is meant to say that the idea of probability is empirical

Probability is based on observation rather than theorizing.

Define probability in terms of relative frequency

Probability is an observation of the relative frequency of a certain outcome.

Define sample space

The set of all possible outcomes.

Define event

Any outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space.

Explain what is meant by a probability model

A mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events.

Construct a tree diagram

9. If you can do one task in x number of ways and a second task in y number of ways, then both tasks can be done in xXy number of ways

10. Sampling with replacement—Taking a sample of a sample space without subtracting the chosen sample from the next sampling.

Sampling without replacement—Taking a sample of a sample space and subtracting the chosen sample from the next sampling, eliminating the given sample from future samplings.

11. 1. Any probability is a number between 0 and 1 2.The sum of the probabilities of all possible outcomes must equal 1

3. If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.

4. The probability that an event does not occur is 1 minus the probability that the event does occur.

12. (AUB)—the event of “A or B”; (A(upside down U)B)—mutually exclusive

13. The two outcomes and the intersection of the two.

14. Being female and being lactose intolerant.

15.

16. 100%

17. If a random phenomenon has k possible…