Probability

1 / 25

# Probability - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Probability' - vidar

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Probability

What is probability?
• 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.

Event is more likely not to occur

Event is more likely to occur

P = 1

Event is certain

to occur

P = 0

Event will not occur

P = .5

Even is equally

likely to occur

or not 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 5
• Rolling 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.
• 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 10
• The 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 non-clubs

# of tens

# of non-tens

# 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

area of smaller object

volume of smaller space

length of smaller segment

total length

total area

total volume

Geometric Probability
• Darts and Bulls-eye