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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.

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9 1 understanding probability

9.1 Understanding Probability

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


Defining probability
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
Terminology

  • Experiment

  • Outcome

  • Sample Space

  • Equally Likely

  • Uniform Sample Space

  • Nonuniform Sample Space

  • Event


Example
Example

Uniform Sample Space


Example1
Example

Nonuniform Sample Space


Defining probability cont
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
Terminology (cont.)

  • Random Event

  • Certain Event

  • Impossible Event

  • Complementary Events

  • Mutually Exclusive Events

  • Non-mutually Exclusive Events


Properties of probability
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
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
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.