Probability Experiments

Two Kinds of Probability

Def: Probability—a numerical measure of the likelihood that a specific event will occur…if the event is A, then the probability of A is denoted as P(A).

certain

The probability of an event occurring lies within the range of zero and one.

Two types of probability

- Experimental probabilities

· Probability estimates arrived at using data gathered through experiments.

- Theoretical probabilities

- The specific value that is approached by experimental probability as more experiments are run.

**reflect back over the penny tossing experiment**

Three Approaches to Computing Probability

- Classical Approach
- Assumes equally likely outcomes, meaning each outcome has the same chance of occurring.

P(A) = _{}

EX: Roll a die

P(5) = 1/6 P(not 4) = 5/6

P(odd) = 3/6 = 1/2 P(prime) = 2/6 = 1/3

**worksheet**

**Rolling Dice**

Not every experiment has equally likely outcomes. Consider the cup-tossing experiment.

Did we have equally likely outcomes?

- Relative Frequency Approach

· Repeat an experiment over and over.

· Record the # of successes.

P(A) = _{}

Law of Large Numbers

If an experiment is performed repeatedly, then the probability obtained from the relative frequency approach approaches the actual or theoretical probability.

**What’s in the Bag**

- Subjective Approach

Consider the following:

A) What
is the probability that

B) What is the probability that you will earn an A in this class?

C) What is the probability that it will rain tomorrow?

Do these questions represent equally likely outcomes?

NO

Do these questions represent experiments that can be conducted over and over so as to produce relative frequencies?

NO

When this happens we have to use subjective probability.

Def: Subjective probability—the probability assigned to an event based on subjective judgment, experience, information, and belief.