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9.1 Understanding ProbabilityPowerPoint Presentation

9.1 Understanding Probability

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### 9.1 Understanding Probability

Remember to Silence Your Cell Phone and Put It In Your Bag!

Defining Probability

- The use of numbers to describe the chance that something will happen.
- The ratio of favorable occurrences to the number of total possible occurrences of an observable event.
- For this class, unless asked to do differently, write your probabilities as simplified fractions

Terminology

- Experiment
- Outcome
- Sample Space
- Equally Likely
- Uniform Sample Space
- Nonuniform Sample Space
- Event

Example

Uniform Sample Space

Example

Nonuniform Sample Space

Defining Probability (cont.)

- Probability, P, of an event A for a uniform sample space:
- Probability, P, of an event A for a nonuniform sample space:

Terminology (cont.)

- Random Event
- Certain Event
- Impossible Event
- Complementary Events
- Mutually Exclusive Events
- Non-mutually Exclusive Events

Properties of Probability

- 0 P(A) 1
- The sum of the probabilities of all outcomes in the sample space is 1
- P(a certain event) = 1
- P(an impossible event) = 0
- If A and B are complementary events, P(A) = 1 – P(B)

Properties of Probability (cont.)

- If A and B are mutually exclusive events, P(A or B) = P(A) + P(B)
- If A and B are non-mutually exclusive events, P(A or B) = P(A) + P(B) – P(A and B)

Law of Large Numbers

- Empirical Probability
- Theoretical Probability
- Law of Large Numbers
- If an experiment is repeated many times, the empirical probability of an event will approach the theoretical probability of the event occurring.

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