Chapter 6.3.2 Probability Models 5

Addition Rule for Disjoint Events: If events A,B,C are disjointed in the sense that no two have any outcomes in common, then P(one or more of A,B,C)=P(A)+P(B)+P(C). This rule extends to any number of disjoint events.
General Addition Rule for Unions of Two Events: P(A or B) = P(A)+P(B) - P(A and B), or P(A U B) = P(A)+P(B) - P(A ∩ B)
The simultaneous occurrence of two events is called a joint event.
The probability of joint events is called a joint probability.
The notation P(A│B) is a conditional probability. That is it gives the probability of one event under the condition tat we know anther event. You can read the bar as "given the information that".
General Multiplication Rule for Any Two Events: The probability that both of the two events A and B happen together can be found by P(A and B) = P(A)P(B│A). Here P(B│A) is the conditional probability that B occurs given the information that A occurs. For both of the two events to occur, first one must occur and then, given that the first event has occurred, the second must occur.
Conditional Probability:P(B│A)= P(A and B) / P(A)
The intersection of any collection of events is the event that all the events occur.
For tree diagrams, the multiplication rule says that the probability of reaching the end of any complete branch is the product of the probabilities written on its segments.
Bayes' Rule: If A and B are any events whose probabilities are not 0 or 1, P(A│B) = P(B│A)P(A) / P(B│A)P(A)+P(B│A^c)P(A^c)
Two events A and B that both have positive probability are independent if P(B│A) = P(B)
This is a good representation of the Venn Diagram you will find in this chapter and how to interpret it.
- The diagram above is set up for conditional events, but will will look very similar for independent events.
- An example would be A representing those who listen to music (50%) , and B being those who watch TV(20%), and those who do both(20%).
- The Pink Half represents Those who, listen to music, but not TV. (50%)
- The Pink and Purple represent those who only listen to music and those who do both. (50%+20%=70%)
- The purple represents Those who do both.(20%)
- The purple and blue represent Those who listen to music and watch TV.(20%+20%=40%)
- And the blue represents those who only watch TV. (20%)
- The outer part of the Venn Diagram would be those who do neither. (10%).
Exercises: 6.54, 6.55-6.61, odd, 6.66-6.77, all

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