12.4 Probabilities of Compound Events
Compound Event – the union or intersection of two events.
Mutually Exclusive Events: if the intersection of events A and B is empty
Probability of Compound Events
• If A and B are two events, then the probability of A or B:
P( A or B) =
•
If A and B are mutually exclusive (meaning no intersection) then the probability of A or B:
P( A or B) =
Example 1: Find the indicated probability. State whether A and B are mutually exclusive.
P ( A ) = 0.4
P ( A ) = 0.25
P ( B ) = 0.35
P ( B ) = _____
P ( A or B ) = 0.5
P ( A and B ) = ____
P ( A or B ) = 0.70
P ( A and B ) = 0
Complement: of event A is denoted A’or A consists of all outcomes that are NOT in A.
Probability of the complement of an event:
• P A' = P A =
( )
()
Example 2: A card is randomly selected from a standard deck of 52 cards.
What is the probability that it is a 10 or a face card?
Example 3: One six-sided die is rolled. What is the probability or rolling a multiple of a 3 or a 5?
Example 4: A card is randomly selected from a standard deck of 52 cards. What is the probability that
the card is a spade or a face card?
Example 5: One six-sided die is rolled. What is the probability of rolling a multiple of 3 or a multiple of 2?
Example 6: When two six-sided dice are tossed, there
are 36 possible outcomes as shown. Find the
probability of the given event.
a.)
The sum is NOT 8
b.)
The sum is greater than or equal to 4
Example 7: A card is randomly selected from a standard deck of 52 cards. Find the probability of the
given event.
a.)
The card is NOT a king
b.)
The card is not an ace or a jack.
Example 8: In a poll of high school juniors, 6 out of 14 took a French class and 11 out of 15 took a
math class. Fourteen out of the 15 took French or math. What is the probability that a student took
both French and math?
Homework: Pg 727 # 20-28even, 29-40, 43, 44