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
→
P(A or B) = P(A) + P(B)
4) The complement rule
states that→
P(A
c
) = 1 – P(A)
5) Two events A and B are independent
→
P(A and B) = P(A)P(B)
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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General 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)
EX 1)
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)
= 0.5
before→
P(A or B) = P(A) + P(B)
(A, B disjoint)
now→
P(A or B) = P(A) + P(B) – P(A and B)
(A, B can have overlap)
EX 2)
random phenomenon→ toss a die (A roll a 1, B roll a 2)
A, B disjoint
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 Spring '11
 Bill
 Conditional Probability, Probability, Pallavolo Modena

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