   Six Sigma Glossary from MiC Quality
Probability
 Bayes Theorem

Let A1, A2,..........Ak be a collection of mutually exclusive and exhaustive possible events. Then for any other possible event 'B': The notation P(A|B) means the probability of 'A' given that 'B' has occurred.

A medical procedure has a 90% probability of correctly diagnosing a medical condition. However if the subject does not have the condition there is a 1% probability of making a faulty diagnosis.

If one person in ten thousand suffers from the condition, what is the probability that a person selected at random who returns a positive result actually suffers from the condition.

The probabilities are:

 Probability A they have the condition B they return a positive result A1 they have the condition 0.0001 A2 they do not have the condition 0.9999 P(B|A1) they return a positive result given that they have the condition 0.90 P(B|A2) they return a positive result when they do not have the condition 0.01 P(A1|B) the probability they have the condition, given the positive result 0.0089

This is highly non-intuitive. The answer stands because the condition is extremely rare, and the number of false positives outweighs the number of correct diagnoses.

 Complementary Probability

The complement of a set A is the set of all outcomes that are not contained in A, denoted by A': Intersection

The outcome of all the events that are in both A and B. Intersection is roughly equivalent to "and":  Multiplication Rules

The multiplication rule states that: There is a 0.01 (1%) probability that a seal will fail if the joint is not coated with a sealing compound before assembly. The proportion of joints that are not coated is 0.05 (5%).

What is the probability that a seal will fail.

 P(A|B) Probability that the seal will fail if not coated 0.01 P(B) Probability the seal will not be coated 0.05 0.01 x 0.05 =0.0005

 Mutually Exclusive

Events that are mutually exclusive, eg. a head and a tail on a coin toss: Probability

The chance of something happening. The probability of getting a head on a coin toss is 0.5.

Probability can also be viewed as the fraction of occurrences over a large number of trials. If the results from many coin tosses are recorded the proportion of heads will be close to 50% (assuming a fair game).

 Union

The outcome of all the events that include A or B. Union is roughly equivalent to "or":  Venn Diagram

A diagram used to illustrate the concepts of probability. Venn diagrams are used in the entries for 'Union', 'Intersection' and 'Complement'.

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