Module 3 Notes

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Probability

There are two basic rules of probability. The first is that the probability associated with any outcome is between zero and one, or between 0% and 100%. A probability of zero or 0% indicates impossibility, while a probability of one or 100% indicates certainty. The second basic rule is that the sum of the probabilities of all the possible events associated with an experiment is one or 100%.

Outcomes must be:

A list of possible outcomes from a random experiment is said to be

exhaustive if there are no other possible outcomes. Following

the second basic rule of probability, the sum of the probabilities of an

exhaustive list of outcomes is one or 100%.

If two outcomes cannot happen at the same time, they are said to be

mutually exclusive. For example, you cannot get both a head and

a tail turning up at the same time when you flip a coin. The outcomes “heads”

and “tails” are therefore mutually exclusive. Similarly, when a product is

inspected after production, it cannot be both “good” and “defective” at the same

time. In this case, the outcomes “good” and “defective” are mutually exclusive.

The multiplication rule for probabilities is derived from

the formula for conditional probability. If two events are independent, the

probability of both events occurring, P(A and B), is a joint

probability and is determined as

P(A and B) = P(A) × P(B)

If two events are dependent, the probability of both events occurring is:

P(A and B) = P(A) × P(B|A) or

P(A and B) = P(B) × P(A|B)

Rearranging the general multiplication rule creates the formula for the

conditional probability of two events:

Review Examples 6.5 and 6.6 on pages 192-193, and note carefully the

difference between selection without and with replacement.

According to the addition rule for probabilities, if you are

interested in the probability of either event A or B occurring (the union of A

and B), you simply add the probability of A occurring to the probability of B

occurring. If events A and B are not mutually exclusive, you need to subtract

their joint probability (the intersection of A and B) from the sum. The notation

for this is

P(A or B) = P(A) + P(B) – P(A and B)

The example for Table 6.3 on page 194 and Example 6.7 on pages 194-195

illustrate the use of the addition rule.

With dependent events you find the probability that two things happen by multiplying the probability of each together. With independent events you find the probability that two things happen by adding the probability of each together.