Download Geometry: Statistics 12.4

Geometry: Statistics 12.4
Two events are disjoint or mutually exclusive if
they have no outcomes in common.
(i.e. ____________________
they do not overlap
Example: A 6-sided die is rolled. Consider if the two
events are disjoint or not disjoint.
a) The result is an even number
The result is a prime number
not disjoint
2 is in both
b) The result is a 2 or a 4
The result is an odd number
disjoint
The union of two events A and B is the set of outcomes
that are in A or B or both
The intersection of two events A and B is
________________________________
the outcomes that are in both A and B
(i.e. the intersection is
_____________________________
where the events A and B overlap
disjoint
P( A)  P( B)  P( A and B)
P( A)  P( B)
Example: A card is randomly chosen from a standard
deck of 52 cards.
a) P(Ace or a face card)
12
4
disjo int
b) P(spade or a face card)
12
13
3 of the face cards are spades
16
 .308
52
13  12  3 22

 .423
52
52
Example: Of the 200 students in a senior class, 113 are either varsity
athletes or on the honor roll. 74 seniors are varsity athletes and 51
seniors are on the honor roll. What is the probability that a randomly
selected senior is both a varsity athlete and on the honor roll?
P(A or B)  P(A)  P(B) - P(A and B)
113
200
74 51
200 200
- 12
 -P(A and B)
200
12
3
P(A and B) 

 .06
200 50
Example: The American Diabetes Association estimates that 8.3% of people in
the U.S. have diabetes. Suppose that a medical lab has developed a simple
diagnostic test for diabetes that is 98% accurate for people who have diabetes
and 95% accurate for people who do not have diabetes (i.e. the test gives a falsepositive).
.98 
.083 D
.02 
.05 
.917 NoD
.95 
.08134
.00166
.04585
.87115
If the laboratory gives the test to a randomly selected person,
what is the probability the test is correct?
.08134  .87115  .95249
If the laboratory gives the test to a randomly selected person,
what is the probability the person has diabetes given the test
result is positive?
P( D and )
P(diabetes | ) 
P()
.08134

 .640
.08134  .04585