Download AP Statistics Section 6.3 A Probability Addition Rules

AP Statistics Section 6.3 A
Probability Addition Rules
Recall these rules of probability:
0
1
1
P(A)  P(B)
1 - P(A)
P(A)  P(B)
Consider the table at the right about Nobel Prize winners. If
one winner is selected at random, find….
215
P(from the U.S.) =
366
135 45
P(in medicine) =

366 122
P (from the U.S. or in medicine) =
215 135 90 260 130




366 366 366 366 183
If events A and B are not disjoint,
then they have some outcomes in
common.
NEW and IMPROVED ADDITION RULE:
P( A)  P( B)  P( A  B)
Note: If A and B are disjoint, then
0
and the Addition Rule above is
obtained.
We can use Venn diagrams to
illustrate non-disjoint events.
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.
Deb
.4
Matt
.3 .2
Find P(Deborah is promoted but Matthew is not)
.4
Find P(that at least one of them is promoted)
P(Deb or Matt)
.7  .5  .3  .9
Find P(neither one is promoted)
1  .9  .1
.2
Example 2: Stephanie is graduating from college.
Here are the probabilities for her obtaining
three jobs.
Example 2: Stephanie is graduating from college.
Here are the probabilities for her obtaining
three jobs.
A
.2
.35
.05
C
0
.1
B
.25
.05
(a) P(Stephanie is offered
at least one of three jobs)
.35  .2  .25  0  .05  .05  .1  1
(b) P(Stephanie is offered jobs A and B but not C)
.2