1. Independent and Dependent Events
19.1

2. Events are independent events if the occurrence of one event does not affect the probability of the other. To find the probability, you multiply the individual probabilities. ( psst … we have already done this).
Below is the formula for calculating the probability of an independent event where A and B are the events.

3. Finding the Probability of Independent Events
A six-sided 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 the probability.
Tossing a 2, then tossing a 2 again.

4. Finding the Probability of Independent Events
A six-sided 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 the probability of
Tossing red, then white, then yellow.

5. Michelle has 6 quarters and 4
dimes in her pocket. Darryl has
2 nickels, 1 quarter, and 5 pennies
in his pocket.
Find the probability that Michelle
selects 1 dime from her pocket and
Darryl selects 1 penny from his pocket.

6. Events are dependent events if the occurrence of one event affects 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 occurred.

7. Finding the Probability of Dependent Events
Two number cubes are rolled–one white and one yellow. Explain why the events are dependant. Then find the indicated probability.
The white cube shows a 6 and the sum is greater than 9 .

8. Finding the Probability of Dependent Events
Two number cubes are rolled–one white and one yellow. Explain why the events are dependant. Then find the indicated probability.
The yellow cube shows an even number and the sum is 5.

9. Finding the Probability of Dependent Events
Two number cubes are rolled–one red
and one blue. Explain why the events are dependent. Then find the indicated
probability.
Blue cube shows a multiple of 3, and the sum is 8
The events are dependent because P(sum of 8) is different when the blue shows a multiple of 3.
P(blue multiple of 3) = 2 6 = 1 3
P(sum is 8| blue multiple of 3) = = 1 6
So, the probability that the blue cube shows a multiple of
3 and the sum is 8 = = 1 18

10. Replacement vs non-replacement
Independent
Bag contains 3 green marbles, 2 red, and 7 blue marbles. A marble is picket at random and is replaced. Then a second marble is picked at random. Find probability that both marbles are blue
Dependent
Bag contains 3 green marbles, 2 red, and 7 blue marbles. A marble is picket at random and is not replaced. Then a second marble is picked at random. Find the probability that both marbles are blue

11. Pop Quiz!!!!! 4 suits are? How many of each suit? How many 5’s?
How many black cards?
What are the face cards?
Who can go win me a million dollars in Vegas?????

12. Example 4: Determining Whether Events Are Independent or Dependant
Two cards are drawn from a deck of 52. Determine whether the events are independent or dependent. Find the probability.

13. Example 4 Continued
A. selecting two hearts when the first card is replaced
B. selecting two hearts when the first card is not replaced
C. a queen is drawn, is not replaced, and then a king is drawn

14. Assignment
19.1 Practice Sheet