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Math1580, chapter 7, probability
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Terms in this set (17)
Outcomes
The most basic possible results of observations or experiments. For example, if you toss two coins, one possible outcome is HT AND OTHER POSSIBLE OUTCOME IS TH
Event
Consists of one or more outcomes that share a property of interest. For example, if you toss two coins and count the number of heads, the outcomes HT and TH both represent the same event of 1 head (and 1 tall).
Single Space
Th set of all possible outcomes of a probability experiment.
Make a __________ for more complex scenarios, such as three flips
Tree diagram
Rules for Probability
1. The probability of an event expressed as P(event), is always between 0 and 1 inclusive.
0 < P (event) < 1 (lines underneath)
2. A probability of 0 means the event is impossible and a probability of 1 means the event is certain.
3. The sum of all probabilities is 1.
Theoretical MethPrinciples d for Equally likely outcomes:
1. _______ the total number of possible outcomes
2. Among all he possible outcomes, count the number of ways the event of interest, A, can occur.
3. Determine the ________, P(A).
P(A) = number of ways A can occur
————————————————-
Total number of outcomes
Count, probability
Suppose there are M possible outcomes for one process and N possible outcomes for a second process. The total number of possible outcomes for the two processes is:
MxN
Example: A restraint offers two choices for an appetizer, five choices for a main course, and three choices for a dessert. How many three-course meals are possible?
2x5x3=30
Relative frequency:
A second way to determine probabilities is to approximate the probability of an event A by making many observations and counting the number of event A occurs. This approach is called ___________________.
P(A) = number of times A occurred
—————————————————
Total number of observations
Empirical method
Based on the assumption that all outcomes are equally likely, is determined by dividing the number of ways an event can occur by the total number of possible outcomes.
Theoretical Probability
Based on observation or experiments, is the relative frequency of Th event of interest.
Relative frequency probability
An estimate based on experience or intuition
Subjective probability
Example: which method is used?
a. I am 100% certain that you'll be happy with this car.
b. Based on government data, the chance of dying in an automobile accident during a one-year period is about 1 in 8000
c. The probability of rolling a 7 with a 12-sided die is 1/12.
a. Subjective
b. Relative Frequency
c. Theoretical
Probability of an event not occurring:
If the probability of an event A is P(A), then the probability that event A does not occur is 1 - P(A). Commonly called the ______________.
Complement
Making a Probability Distribution:
A ____________ represents the probabilities of all possible events. To make a probability distribution, do the following:
1. List all possible outcomes. Use a table of figure if it is helpful
2. Identify outcomes that represent the same event and determine the probability of each event
3. Make a table if each event and its probability. The sum of all probabilities must be 1.
Probability distribution
Odds:
________ are the ratio of the probability that a particular event will occur to the probability, that it will not occur.
The odds for an event A are p(A)
——-
P(not A),
We can also write this as n(A): n(not A)
The odds against an event A are P(not A)
—————
P(A),
We can also write this as n(not A): n (A)
Note: in gambling, the term _________ generally means the _________
Odds, odds, odds against
Two events are ______ if the outcome of one does not affect the probability of the other event.
If two independent events A and B have individual probabilities P(A) and P(B)
...
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