Transcript Addition Rules for Probability

MATH 1107
Elementary Statistics
Lecture 5
Addition Rules in Probability
Addition Rules in Probability
Lets say that in order to maintain your HOPE
scholarship, you must obtain either an A or a B in this
class. Putting aside study time and unforeseen
events, what is the probability of this occurring?
Addition Rules in Probability
Since you cannot obtain both an A and a B,
these are mutually exclusive events…or
disjointed events
So, the Prob (A or B) = P(A)+P(B)
If your grade is random, then the answer is:
Prob (A or B) = 1/5 + 1/5 = 2/5 or 40%
Addition Rules in Probability
Now lets say that in order to retain your scholarship,
you must pass either Statistics or English. What is
the probability of this?
Addition Rules in Probability
Since you can obtain passing grades in both,
this is not considered a disjointed event. The
probability for this outcome is:
P(A or B) = P(A) + P(B) – P(A and B), where
P(A and B) is the probability of passing both
courses. This probability must be deleted to
prevent double counting.
Addition Rules in Probability
P(A)
P(A and B)
P(B)
Addition Rules in Probability
Passengers on the Titanic
Men
Women
Boys
Girls
Total
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
Total
1692
422
64
56
2223
What is the probability of selecting a man or a boy from
the passenger list at random (regardless of their eventual
fate)?
Addition Rules in Probability
Passengers on the Titanic
Men
Women
Boys
Girls
Total
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
Total
1692
422
64
56
2223
P(man or boy) = 1692 + 64 = 1756 or 79%
2223 2223 2223
This is an example of a disjointed events.
Addition Rules in Probability
Passengers on the Titanic
Men
Women
Boys
Girls
Total
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
Total
1692
422
64
56
2223
What is the probability of selecting a man or a survivor from
the passenger list at random?
Addition Rules in Probability
Passengers on the Titanic
Men
Women
Boys
Girls
Total
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
Total
1692
422
64
56
2223
P(man or survivor) = 1692 + 706 - 332 = 2066 or 93%
2223 2223 2223 2223
This is an example of events that are not disjointed.
Addition Rules in Probability
What is the probability of selecting a subject who is
pregnant or tested positive?
Positive Test
Negative Test
Pregnant
80
5
Not Pregnant
3
11
P(Preg or + Test) = 80 + 5 + 3 = 88 or 89%
99 99 99 99
P(Preg or + Test) = 83 + 85 - 80 = 88 or 89%
99
99 99 99
Addition Rules in Probability
Positive Test
Negative Test
Pregnant
80
5
Not Pregnant
3
11
False Positive
False Negative