1. Ch 11 – Probability & Statistics
11.3 – Independent and Dependent Events

2. Probability of Independent Events
Events are independent events if the occurrence of one event does not affect the probability of the other.
Probability of Independent Events
If A and B are independent events, then

3. A six-sided number cube is labeled with the numbers 1, 2, 2, 3, 3, and 3. Four sides are colored red, one side is white, and one side is yellow. Find each probability.
Tossing 2, then 2
B. Tossing red, then white, then yellow

4. Probability of Dependent Events
Events are dependent events if the occurrence of one event affect the probability of the other.
To find the probability of dependent events, you can use conditional probability P(B|A), the probability of event B, given that event A has already occurred.
Probability of Dependent Events
If A and B are dependent events, then

5. Two number cubes are rolled—one blue and one yellow
Two number cubes are rolled—one blue and one yellow. Explain why the events are dependent. Then find the indicated probability. 1 2 3 4 5 6
The blue cube shows a 6 and the sum is greater than 9.
The yellow cube shows an even number and the sum is 5.

6. Domestic Migration by Region
The table shows domestic migration from 1995 to A person is randomly selected. Find each probability.
Domestic Migration by Region
(thousands)
Region
Immigrants
Emigrants
Northeast
1537
2808
Midwest
2410
2951
South
5042
3243
West
2666
2654
That an emigrant is from the West
That someone selected from the South is an immigrant
That someone selected is an emigrant and is from the Midwest

7. What do you know about face cards?
52 Cards Total
2 Colors
Red 26 cards
Black 26 cards
4 Suits
Hearts ♥ Red 13 cards
Diamonds ♦ Red 13 cards
Clubs ♣ Black 13 cards
Spades ♠ Black 13 cards
4 cards of each Number
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King

8. Replacement?
Two cards are drawn from a deck of 52. Determine whether the events are independent or dependent. Find the probability.
Selecting two hearts when the first card is replaced
Selecting two hearts when the first card is not replaced
A queen is drawn, is not replaced, and then a king is drawn