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4.5
General Probability Rules
Previous Probability Rules
1) The probability P(A) of any event A satisfies 0
≤
P(A)
≤
1.
2) All possible outcomes together must have probability 1.
P(S) = 1.
3) Two events A and B are disjoint
if they have no outcomes in common and so can
never occur together.
If A and B are disjoint,
P(A or B) = P(A) + P(B)
This is the addition rule for disjoint events
.
4) The complement
of any event A is the event that A does not occur, written as A
c
.
The
complement rule
states that
P(A
c
) = 1 – P(A)
5) Two events A and B are independent if knowing that one occurs does not change the
probability that the other occurs.
If A and B are independent,
P(A and B) = P(A)P(B)
This is the multiplication rule for independent events
.
General addition rules
The union
of any collection of events is the event that at least one of the collection
occurs.
Addition rule for disjoint events (Figure 4.16)
If events A, B, and C are disjoint 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.
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View Full DocumentGeneral addition rule for unions of two events
For any two events A and B,
P(A or B) = P(A) + P(B) – P(A and B)
Figure 4.18
EX)
random phenomenon toss a die (A roll a 1, B roll an odd #)
P(A or B) = P(get 1, 3, or 5) = 0.5
P(A or B) = P(A) + P(B) – P(A and B)
P(A or B) = (1/6) + (3/6) – (1/6)
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 Spring '08
 ABDUS,S.

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