Stats CH 4 Quiz

how to find mutually exclusive events

1. define the experiment 2. define the outcomes for a single trial of the experiment 3. define the sample space 4. determine whether the events are mutually exclusive

How to create a tree diagram

1. define the experiment 2. define the outcomes for a single trial of the experiment 3. define the sample space for three trials using a tree diagram

how to set up a sample space

1. define the experiment 2. list the outcomes associated with one trial of the experiment 3. define the sample space 4. define the event of interest

experiment

A process that produces a single outcome whose result cannot be predicted with certainty

Probability Rule 4

Addition for any two events E1 and E2 P(E1 or E2) = P(E1) + P(E2) - P9E1 and E2) - use this rule when there is the word OR; it indicates addition -ex: "there is a 0.40 chance that a respondent will preform 1 to 2 searches OR be in the over-50 age group."

classical probability example

Consider again the experiment of flipping a coin one time. There are two possible outcomes: head and tail. If we assume the coin is fair, then each outcome is equally likely. Thus, with the classical assessment method, the probability of a head is the ratio of the number of ways a head can occur (1 way) to the total number of ways any outcome can occur (2 ways). Thus we get P1Head2 = 1 way 2 ways = 1 2 =0.50 The chance of a head occurring is 1 out of 2, or 0.50

what is the joint probability of two independent events?

- it is simply the product of the probabilities of the two events.

Probability rule 6

For any two events E1 and E2. P(E1lE2) = P(E1 and E2)/P(E2) - used to determine the chances of two or more events occuring either at the same time or in succession. -ex: a quality control manager for a manufacturing compnay may be interested in the prob of selecting two successive defective products from an assembly line - uses a joint probability P(E1 and E2), and a marginal probability, P(E2), to calculate the conditional probability P(E1lE2)

Probability rule 5

For two mutually exclusive events E1 and E2. P(E1 or E2) = P(E1) + P(E2)

Probability rule 9: multiplication rule for independent events

P(E1 and E2) = P(E1)P(E2) - use this rule if the two events of interest are independent, the imposed condition does not alter the probability, and the multiplication rule takes the form of the rule - it is the primary way that you can determine whether any two events are independent

Probability rule 8: multiplication rule for any two events

P(E1 and E2) = P(E1)P(E2lE1) - Use this rule to find the joint probability of two events in the discussion on addition of two events and in the discussion on conditional probability

which rules are the complement rule most closely connected with

Rules 1 & 2 P(E) = 1 - P(E) that is, the probability of the complement of event E is 1 minus the probability of event E

sample space

The collection of all outcomes that can result from a selection, decision, or experiment

complement

The complement of an event E is the collection of all possible outcomes not contained in event E.

relative frequency assessment

The method that defines probability as the number of times an event occurs divided by the total number of times an experiment is performed in a large number of trials.

subjective probability assessment

The method that defines the probability of an event as reflecting a decision maker's state of mind regarding the chances that the particular event will occur.

conditional probability

The probability that an event will occur given that some other event has already happened

classical probability assessment

Two events are dependent if the occurrence of one event impacts the probability of the other event occurring.

dependent events

Two events are dependent if the occurrence of one event impacts the probability of the other event occurring.

independent events

Two events are independent if the occurrence of one event in no way influences the probability of the occurrence of the other event

mutually exclusive events

Two events are mutually exclusive if the occurrence of one event precludes the occurrence of the other event

event

a collection of experimental outcomes

Probability rule 1

all possible outcomes associated with an experiment from the sample space. therefore, the sum of all the probabilities of all possible outcomes is 1.

when past data are not available to help make decisions:

decision makers must make a subjective probability assessment to measure a personal conviction that an outcome will occur

rule 7: conditional probability for independent events

for independent events E1 and E2, P(E1lE2) = P(E1) P(E2) > 0 and P(E2lE1) = P(E2) P(E1) > 0 - probability rule 7 shows the conditional probability of one event occurring, given that a second independent event has already occurred, is simply the probability of the event occurring

addition rule for individual outcomes

if a single event is made up of two or more individual outcomes, then the probability of the event is found by summing the probabilities of the individual outcomes

What is an example of an experiment in a business sitution?

it could be like an investment decision, a personnel decision, or a choice of warehouse location

probability rule 2

k = number of outcomes in the sample ei = ith outcome

Probability

the chance that a particular event will occur. the probability value will be in the range 0 to 1. A value of 0 means the event will not occur. A probability of 1 means the event will occur. Any number between 0 and 1 reflects the uncertainty of the event occurring. The definition given is for a countable number of events.

probability rule 3

the probability of an event Ei is equal to the sum of the probabilities of the individual outcomes that form Ei. Ex: if Ei = {e1 + e2 + e3} then, P(E1) = P(e1) + P(e2) + P(e3)