stats 4
What is probability rule 3?
If an event is certain, then the probability of E is 1
What is the rule for complementary events?
If the probability of an event or the probability of its complement is known, then the other can be found by subtracting the probability from 1
what is a tree diagram?
A device consisting of line segments emanating from a starting point and also from the outcom point. It is used to determine all possible outcomes of a probability experiment
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When a single die is rolled, what is the probability of getting a number less than 7? What probability rule is this?
1,2,3,4,5,6, are less than 7 so 6/6=1 so the event of getting a number less than 7 is certain--prob rule 3
What are the 3 basic interpretations of probability?
1. Classical probability 2. Empirical or relative frequency probability 3. Subjective probability
What are equally likely events?
Events that have the same probability of occuring
What is probability rule 2?
If an event E cannot occur (event contains no members in the sample space) its probability is 0 ex. when a single die is rolled, what is the probability of getting a 9?---sample space>1,2,3,4,5,6, hence 9 is impossible to get
In a probabilty experiment, what are the possible outcomes?
The possible outcomes cannot be negative, greater than one, or greater than 100%, other than that they can assume any value.
What is the give statemen an example of ?
it is an example of empirical probability
What is Empirical probability?
relies on actual experience to determine the likelihood of outcomes.
What is a sample space?
set of all possible outcomes of a probability experiment Ex. roll of a single die- there are 6 possible outcomes-1,2,3,4,5,6
What is a compound event?
the event of getting an odd number
What is an outcome?
the result of a single trial of a probability experiment
What is a complement of an event E?
the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by E with a bar over it. Ex. getting a odd number when rolling a die
What is Subjective probability?
uses a probability value based on an educated guess or estimate, employing opinions and inexact information.
Can empirical probabilities be found using a relative frequency distribution?
yes
What is a simple event?
An event with one outcome
In venn diagrams the inside and the outside of the circle represents?
Area inside represents the probability of event E, P(E) Area outside represents the probability of all the events in the sample space P(S)
What is the difference between classical and empirical probability?
Classical probability assumes that certain outcomes are equally likely (such as die rolled), while empirical probability relies on actual experience to determne the likelihood of outcomes
What are the rounding rules for probabilities?
Probabilities should be expressed as reduced fractions or rounded to 2 or 3 decimal places ex. -0.0000587 to 0.00006
What is probability rule 4?
The sum of the probabilities of all the outcomes in the sample space is 1
What is a probability experiment?
a chance process that leads to well-defined results called outcomes
What is an event?
a set of outcomes of a probability experiment -ecent can be one outcome or more than one outcome ex.die rolled and 6 show this result is called an outcome,since it is a result of a single trial
What is the law of large numbers?
as the number of trials increases, the expirical probability of will approach the theoretical probability
What is classical probability?
assumes that all outcomes in the sample space are equally likely to occur. -uses sample spaces to determine the numerical probability that an event will happen.
What is probability rule 1?
event E is a number (either a fraction or decimal) between and including 0 and 1 --so can not be negative or greater than 1
What is the formula for empirical probability?
given a frequency distribution, the probability of an event being in a given class is frequency for the class =f total frequencies in the distribution n ---f/n
