Transcript Algebra 2 Lesson 9

9.7 – Probability of
Multiple Events
Consider the Following:
A
marble is picked at random from a
bag. Without putting the marble
back, a second one has chosen. How
does this affect the probability?
 A card is picked at random from a
deck of cards. Then a dice is rolled.
How does this affect the probability?
Outcomes of Different Events
 When
the outcome of one event
affects the outcome of a second
event, we say that the events are
dependent.
 When one outcome of one event
does not affect a second event, we
say that the events are independent.
Probability of Multiple Events
Classify each pair of events as dependent or independent.
a. Spin a spinner. Select a marble from a bag that contains marbles
of different colors.
Since the two events do not affect each other, they are independent.
b. Select a marble from a bag that contains marbles of two colors.
Put the marble aside, and select a second marble from the bag.
Picking the first marble affects the possible outcome of picking the
second marble. So the events are dependent.
Decide if the following are
dependent or independent
 An
expo marker is picked at
random from a box and then
replaced. A second marker is
then grabbed at random.
 Two dice are rolled at the
same time.
 An Ace is picked from a deck
of cards. Without replacing it,
a Jack is picked from the
deck.
Independent
Independent
Dependent
How to find the Probability of Two
Independent Events
 If
A and B are independent events,
the P(A and B) = P(A) * P(B)
 Ex:
If P(A) = ½ and P(B) = 1/3 then
P(A and B) =
1 1 1
 
2 3 6
Mutually Exclusive Events
 Two
events are mutually exclusive
then they can not happen at the
same time.
Probability of Multiple Events
Are the events mutually exclusive? Explain.
a. rolling an even number or a prime number on a number cube
By rolling a 2, you can roll an even number and a prime number
at the same time.
So the events are not mutually exclusive.
b. rolling a prime number or a multiple of 6 on a number cube
Since 6 is the only multiple of 6 you can roll at a time and it is not a prime
number, the events are mutually exclusive.
How to find the Probability of Two
Mutually Exclusive Events
 If
A and B are mutually exclusive
events, then P(A or B) = P(A) + P(B)
Let’s Try One
At a restaurant, customers get to choose one of
four desserts. About 33% of the customers
choose Crème Brule, and about 28% Chocolate
Cheese Cake. Natasha is treating herself for
pole vaulting nine feet at the meet. What is the
probability that she will choose Crème Brule or
Chocolate Cheese Cake?
Are the events mutually exclusive?
Solution:
.33 + .28 = .61 = 61%
Yes. So:
P(A) + P(B)