1. 9.7 – Probability of Multiple Events

2. 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?

3. 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.

4. 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.

5. 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

6. 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) =

7. Mutually Exclusive Events
Two events are mutually exclusive then they can not happen at the same time.

8. 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.

9. 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)

10. Let’s Try One Solution: .33 + .28 = .61 = 61%
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?
Yes. So:
P(A) + P(B)
Are the events mutually exclusive?
Solution:
= .61 = 61%

11. Let’s Try One
A spinner has 20 equal size sections numbered from 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?
Are the events mutually exclusive?