Transcript Addition Rules for Probability

Addition Rules for Probability
Mutually Exclusive Events
When do you add/ when do you
subtract probabilities?
Mutually Exclusive Events
• Two events are considered mutually
exclusive if they cannot occur at the same
time on a single trial.
• No outcomes in common.
• Examples:
•
•
•
•
heads/tails
Odd #/Even #
2 or 3 in deck of cards
Red or black card
Mutually Exclusive Events
• When 2 events A and B are mutually exclusive
the probability that either A or B will occur on a
single trial is:
• P(A or B) = P(A) + P(B)
• Example 1: A bag contains 3 red, 2 blue and 5
green balls. A single ball is drawn from the bag.
Find the probability of selecting either a red or
green ball.
• P(R or G) = P(R) + P(G)
3 5
8

10 10

10
Example 2: Mutually Exclusive
• In a recent year, 45% of voters in PA were
registered Democrat, 40% were registered
Republican and 15% were registered
Independent. Find the probability that if a voter
is selected at random, he is registered either
Republican or Independent.
• P(R or I) = P(R) + P(I)
=40% + 15% = 55%
Non-Mutually Exclusive Events
• Two events are not mutually exclusive if it
is possible for the events to occur at the
same time on a single trial.
• Have at least one outcome in common.
• Examples:
• 3 or odd #
• Jack or red card
• female or senior
Non-Mutually Exclusive Events
• When 2 events A and B are not mutually
exclusive the probability that either A or B will
occur on a single trial is:
• P(A or B) = P(A) + P(B) – P(A and B)
• Example 1: A Card is drawn from a standard deck
of cards. Find the probability of selecting either a
2 or a heart.
• P(2 or H) = P(2) + P(H) – P(2 and H)
4 13 1 16
 

52 52 52 52
Example 2: Non-Mutually Exclusive
• A study of patient records at a public health
clinic showed that 15% of the patients had a
dental exam, 45% had a general physical and
5% had both. If a patient’s record is randomly
selected, what is the probability that the patient
received either a dental exam or a physical?
• P(D or P) = P(D) + P(P) – P(D and P)
=15% + 45% - 5% = 55%
Other Examples 1
• The probability that a customer at an ice
cream shop selects sprinkles or hot fudge
is .43, and the probability that the
customer selects sprinkles only is .32. If
the probability that he or she selects hot
fudge only is .17, find the probability of the
customer selecting both items.
P(S or F) = P(S) + P(F) – P(S and F)
.43 = .32 + .17 – P(S and F)
.06= P(S and F)
Other Examples 2
• The Bargain Auto Mall has these cars in
stock. If a car is selected at random, find the
probability that it is
• a. Domestic
• b. Foreign and Mid-size
• c. Domestic or an SUV
SUV
Compact Mid-Sized
Foreign
20
50
20
Domestic
65
100
45
Solution – Other Example 2
SUV
Compact
Mid-Sized
Foreign
20
50
20
Domestic
65
100
45
•
a)
b)
c)
Sample space = 300
P(D) = 210/300
P(F and M) = 20/300
P(D or an SUV) = 230/300