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).
The probability of an event occurring lies within the range of zero and one.
Two types of probability
· Probability estimates arrived at using data gathered through experiments.
**reflect back over the penny tossing experiment**
Three Approaches to Computing Probability
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
Not every experiment has equally likely outcomes. Consider the cup-tossing experiment.
Did we have equally likely outcomes?
· Repeat an experiment over and over.
· Record the # of successes.
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**
Consider the following:
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?
Do these questions represent experiments that can be conducted over and over so as to produce relative frequencies?
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.