1. Classify each pair of events as dependent or independent.
Probability of Multiple Events
LESSON 9-7
Additional Examples
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.

2. Relate: probability of both events is probability of first event
Probability of Multiple Events
LESSON 9-7
Additional Examples
A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get a blue marble and a black marble? 30 50 47 57
Relate:  probability of both events is probability of first event
times probability of second event
Define: Event A = first marble is blue. Then P(A) =
Event B = second marble is black. Then P(B) =
Write: P(A and B) = P(A) • P(B)

3. P(A and B) = • = Multiply. = Simplify.
Probability of Multiple Events
LESSON 9-7
Additional Examples
(continued)
P(A and B) = • 30 50 47 57
1410
2850
= Multiply.
= Simplify. 47 95
The probability that a blue and a black marble will be drawn is , or 49%. 47 95

4. Mutually Exclusive Formulas
Probability of (A or B)
Mutually Exclusive means that it is not possible for two events to happen at the same time.
If A and B are mutually exclusive events, then
P (A or B)= P(A) + P(B)
If A and B are not mutually exclusive events, then
P(A or B) = P(A) + P(B) – P(A and B)

5. Are the events mutually exclusive? Explain.
Probability of Multiple Events
LESSON 9-7
Additional Examples
Are the events mutually exclusive? Explain.
a. rolling an even number and rolling a number greater
than 5 on a number cube
By rolling a 6, you can roll an even number and a
number greater than 5 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.

6. What is the probability that a customer will choose beans or spinach?
Probability of Multiple Events
LESSON 9-7
Additional Examples
At a restaurant, customers get to choose one of four vegetables with any main course. About 33% of the customers choose green beans, and about 28% choose spinach.
What is the probability that a customer will choose beans or spinach?
Since a customer cannot not choose both beans and spinach,
the events are mutually exclusive.
P(beans or spinach) = P(beans) + P(spinach)   Use the P(A or B)
formula for mutually
exclusive events. =
= 0.61
The probability that a customer will choose beans or spinach
is about 0.61 or about 61%.

7. P(multiple of 2 or 3) = P (multiple of 2) +
Probability of Multiple Events
LESSON 9-7
Additional Examples
A spinner has twenty equal-size sections numbered from 1 to 20. If you spin the spinner, what is the probability that the number you spin will be a multiple of 2 or a multiple of 3?
P(multiple of 2 or 3) = P (multiple of 2) +
P (multiple of 3) – P (multiple of 2 and 3)
= + – 10 20 6 3 = 13 20
The probability of spinning a multiple of 2 or 3 is . 13 20