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AP Statistics Section 6.3 A
Probability Addition Rules
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Recall these rules of probability:
0 1 1
P(B)P(A)
P(A)-1
P(B)P(A)
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Consider the table at the right about Nobel Prize winners. If one winner is selected at random, find….
P(from the U.S.) =
P(in medicine) =
P (from the U.S. or in medicine) =
366
215
122
45
366
135
366
135
366
215
183
130
366
260
366
90
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If events A and B are not disjoint, then they have some outcomes in
common.
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NEW and IMPROVED ADDITION RULE:
Note: If A and B are disjoint, then
and the Addition Rule above is obtained.
)()()( BAPBPAP
0
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We can use Venn diagrams to illustrate non-disjoint events.
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Example 1: The probability that Deborah is promoted, P(D) , is 0.7. The probability that Matthew is promoted,
P(M) , is 0.5. The probability that both Deborah and Matthew are promoted, P(D and M), is 0.3.
3.Deb
.4Matt
.2
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Find P(Deborah is promoted but Matthew is not)
4.
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Find P(that at least one of them is promoted)
Matt)or P(Deb
9.3.5.7.
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Find P(neither one is promoted)
1.9.1
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2.
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Example 2: Stephanie is graduating from college. Here are the probabilities for her obtaining three jobs.
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Example 2: Stephanie is graduating from college. Here are the probabilities for her obtaining three jobs.
A B
C
0
2.
05. 05.
35. 25.
1.
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(a) P(Stephanie is offered at least one of three jobs)
(b) P(Stephanie is offered jobs A and B but not C)
11.05.05.025.2.35.
2.