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PROBABILITY
What is probability?
In your own words… Probability of an event is the number
from 0 to 1 that indicates the likelihood the event will occur.
An event is an outcome or collection of outcomes
Probabilities can be written as a decimal, a percent, or a fraction.
What is probability?
For example, when rolling a dice there are six possible outcomes or events: 1, 2, 3, 4, 5, or 6.
A different event could be “rolling an odd number”. So, the event would be 1, 3, or 5
Probability
Using a number line can help describe the probability of an event.
P = 0Event will not occur
P = .5Even is equally likely to occuror not occur
P = 1Event is certainto occur
Event is more likely not to occur Event is more
likely to occur
Theoretical Probability
When all outcomes are equally likely, the theoretical probability that an event A will occur is:
P(A) = number of outcomes in event A ÷ Total number of outcomes
The theoretical probability of an even tis often simply called the probability of the event.
Find Probabilities of an Event You roll a standard six-sided die. Find to
probability of:Rolling a 5Rolling an even number
Find Probabilities of an Event There are 6 possible outcomes. Only 1
outcome corresponds to rolling a 5.
P(rolling a 5) = =# of ways to roll a 5
# of ways to roll the die
Find Probabilities of an Event Find the probability of rolling an even
number. A total of 3 outcomes correspond to
rolling an even number: a 2, 4, or 6
P(rolling even number) =
=
# of ways to roll an even number
# of ways to roll the die
Find Probabilities of an Event You have an equally likely chance of
choosing any integer from 1 through 20. Find the probability of the given event.
A perfect square is chosen. A factor of 30 is chosen.
Answers
A perfect square is chosen
A factor of 30 is chosen
Use Permutations or Combinations A community center hosts a talent
contest for local musicians. On a given evening, 7 musicians are scheduled to perform. The order in which the musicians perform is randomly selected during the show.
Use Permutations or Combinations What is the probability that the
musicians perform in alphabetical order by their last names? (Assume that no two musicians have the same last name)
Use Permutations or Combinations There are 7! different permutations of
the 7 musicians. Of these, only 1 is in the alphabetical order by last name.
So the probability of is:
P(alphabetical order) =
Use Permutation or Combinations You are friends with 4 of the musicians.
What is the probability that the first 2 performers are your friends?
Use Permutations and Combinations There are 7C2 different combinations of 2
musicians. Of these, 4C2 are 2 of your friends.
So, the probability is:
P(first 2 performers are your friends) =
Odds
You can also use odds to measure the likelihood that an event will occur.
Odds measure the chances in favor of an event occurring or the chances against an event occurring.
Odds
When all outcomes are equally likely, the odds in favor and not in favor of an event A are as follows:
Odds in favor of event A =
Odds not in favor of event A =
You can write the odds in favor of or against an event in the form or in the form a:b.
# of outcomes in A
# of outcomes not in A
# of outcomes not in A
# of outcomes in A
Find odds
A card is drawn from a standard deck of 52 cards. Find:The odds in favor of drawing a 10The odds against drawing a club
Find odds Odds in favor of drawing a 10 =
= or 1:12
Odds against drawing a club =
= or 3:1
# of tens
# of non-tens
# of non-clubs
# of clubs
Find Odds
What are the odds:In favor of drawing a heart
Against drawing a queen
Experimental Probability
Sometimes it is not possible or convenient to find the theoretical probability of an event.
In such cases, you may be able to calculate an experimental probability by performing an experiment, conducting a survey, or looking at the history of the event.
Experimental Probability
When an experiment is performed that consists of a certain number of trials, the experimental probability of an event A is given by:
P(A) = # of trials where A occurs
Total # of trials
Geometric Probability
Some probabilities are found by calculating a ratio of two lengths, areas, or volumes.
These are called geometric probabilities
Geometric Probability
Length
Area
Volume
length of smaller segment
total length
area of smaller object
total area
volume of smaller space
total volume
Geometric Probability
Darts and Bulls-eye
