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Three types of Probability

1. Theoretical probability: For theoretical reasons, we assume that all n possible outcomes of a particular experiment are equally likely, and we assign a probability of [pic] to each possible outcome. Example: The theoretical probability of rolling a 3 on a regular 6 sided die is 1/6.

2. Relative frequency interpretation of probability: We conduct an experiment many, many times. Then we say

[pic]

Relative Frequency is based on observation or actual measurements.

Example: A die is rolled 100 times. The number 3 is rolled 12 times. The relative frequency of rolling a 3 is 12/100.

3. Personal or subjective probability: These are values (between 0 and 1 or 0 and 100%) assigned by individuals based on how likely they think events are to occur. Example: The probability of my being asked on a date for this weekend is 10%.

Probability Rules

1. The probability of an event is between 0 and 1. A probability of 1 is equivalent to 100% certainty. Probabilities can be expressed at fractions, decimals, or percents.

0 ≤ pr(A) ≤ 1

2. The sum of the probabilities of all possible outcomes is 1 or 100%. If A, B, and C are the only possible outcomes, then pr(A) + pr(B) + pr(C) = 1

Example: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. pr(red) + pr(blue) + pr(green) = 1 [pic]

3. The sum of the probability of an event occurring and it not occurring is 1. pr(A) + pr(not A) = 1 or pr(not A) = 1 - pr(A)

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Example: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.

pr (red) + pr(not red) = 1 [pic] pr (not red) = [pic]

4. If two events A and B are independent (this means that the occurrence of A has no impact at all on whether B occurs and vice versa), then the probability of A and B occurring is the product of their individual probabilities.

pr (A and B) = pr(A) · pr(B)

Example: roll a die and flip a coin. pr(heads and...