STA220H5 Chapter Notes - Chapter 3.2: Mutual Exclusivity
3.2-3.4
The union of two events A and B is the vent that occurs if either A or B (or both)
occurs on a single performance of the experiment. The denote the union of events A
and B by the symbol A U B. A U B consists of all the sample points that belong to A or
B or both. (See Figure 3.7a.)
The intersection of two events A and B is the event that occurs if both A and B occur
on a single performance of the experiment. We write A ^ B for the intersection of A
and B. A ^ B consists of all the sample points belonging to both A and B. (see figure
3.7b.)
The complement of an event A is the event that A does not occur- that is, the event
consisting of all sample points that are not in event A. We denote the complement of
A by Ac.
Rule of complements
The sum of the probabilities of complementary events equals 1; that is,
P (A) + P (Ac) = 1
Additive rule of probability
The probability of the union of events A and B is the sum of the probability of event
A and the probability of event B, minus the probability of the intersection of events
A and B; that is,
Events A and B are mutually exclusive if A ^ B contains no sample points-that is, if A
and B have no sample points in common. For mutually exclusive events,
Probability of union of two mutually exclusive events
If two events A and B are mutually exclusive, the probability of the union of A and B
equals the sum of the probability of A and the probability of B; that is,
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Document Summary
The union of two events a and b is the vent that occurs if either a or b (or both) occurs on a single performance of the experiment. The denote the union of events a and b by the symbol a u b. A u b consists of all the sample points that belong to a or. The intersection of two events a and b is the event that occurs if both a and b occur on a single performance of the experiment. We write a ^ b for the intersection of a and b. A ^ b consists of all the sample points belonging to both a and b. (see figure. The complement of an event a is the event that a does not occur- that is, the event consisting of all sample points that are not in event a. The sum of the probabilities of complementary events equals 1; that is,
