Page 220 - Algebra 1

Type of Events
Definition
Calculating the Probability
Independent Events
The outcome of the first event does not affect the second event.
P(A and B) = P(A) · P(B)
Dependent Events
The outcome of the first event does affect the second event.
P(A and B) = P(A) · P(B), where P(B) is calculated under the new conditions.
Example
1
Identifying Situations Involving Independent and Dependent Events
Identify each set of events as independent or dependent.
a. rolling a 6 on one number cube and a 4 on another number cube
SOLUTION These events are independent. Rolling one number cube does not affect the outcome of rolling the other number cube.
b. rolling a 6 on a number cube and then a 4 on the same number cube
SOLUTION These events are independent. Both rolls of this number cube have the same possible outcomes, and the result of the first roll does not affect the second roll.
c. drawing a red marble from a bag, keeping it out of the bag, and then drawing a blue marble
SOLUTION These events are dependent. By not replacing the first marble, the outcome of the second draw is affected. There are fewer marbles to choose from.
d. drawing a red marble from a bag, putting it back in the bag, and then drawing a blue marble
SOLUTION These events are independent. Because the first marble is replaced, the second draw is not affected. It has the same choices as the first.
A tree diagram can help demonstrate the sample space for events.
Using a Tree Diagram
A coin is flipped twice. Make a tree diagram showing all possible outcomes. What is the probability of the coin landing on heads both times?
Hint
Sometimes independent events are described as events with replacement. Dependent events are without replacement.
Example
2
SOLUTION
First
H
T
Second Outcomes P(H, H) = _1 HHH4
THT HTH
TTT
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