12-7
Probability of Compound Events
A compound event is made up of two or
more simple events.
These events can be independent or
dependent events.
Independent events: The outcome of one
event does not affect the outcome of the
other.
Example: Sam is flying from Detroit to Miami.
The airline reports this flight has a 45% ontime record.
The airline also reports that they lose luggage
7% of the time.
A
B
P(A and B)
P(A and B) = P(A) P(B)
For independent events!
Dependent Events: When the outcome of
one event affects the outcome of another
event.
Example: A bag contains 6 black marbles,
9 blue marbles, and 4 yellow marbles. A
marble is selected, and then without
replacement, a second marble is selected.
What is the probability of selecting a yellow
marble and then a blue marble?
P(A and B) = P(A) P(B following A)
For dependent events!
Mutually Exclusive Events:
Events that cannot occur at the same time.
A
B
P(A or B)
P(A or B) = P(A) + P(B)
A die is rolled.
Find the probability of rolling a 3 or 5
Examples:
A bag contains 6 black marbles, 9 blue,
4 yellow, and 2 green.
A marble is selected, replaced, and then a
second marble is selected.
Find P(black, yellow)
P(not black, blue)
Carl randomly draws three cards from a deck
of cards one at a time, without replacement.
Find:
P(diamond, spade, diamond)
P(four, four, not a jack)
A card is drawn from a standard deck of cards.
Find
P(7 or 8)
Probability of events that are not mutually exclusive:
Find the probability of randomly drawing a 2 or
a diamond from a deck of cards.
Twos
2
2
2
P(2)
Diamonds
A 3 4 5
2
6 7 8 9
10
J
Q K
P(diamond)
P(2
)
P(2 or diamond) = P(2) + P(diamond) - P(2 )