Name: ______Date: ______Period: ____
MCC7.SP.8: Probabilities of Compound Events
Compound Event: ______
______
Using a table with Compound Events
EXAMPLE 1: If I toss two fair coins at the same time, is the probability that both coins will land on heads ½?
First, use the table to find the sample space for tossing two coins at the same time.
Heads (H) / Tails (T)Heads (H)
Tails (T)
Second, find out how many possible outcomes are in the sample space. ______
Third, Circle the outcomes that show both coins landing on heads.
Fourth, determine how many favorable outcomes there are. ______
Finally, determine the probability of both coins landing on heads. ______
EXAMPLE 2: Leo and Paul have 5 cards. Leo’s cards are numbered 1, 3, 4, 5, 5. Paul’s cards are numbered 1, 2, 3, 4, 6. Without looking, they each choose one card to show. The greater card wins. Make a table and list all possible outcomes.
What is Leo’s probability of winning? What is Paul’s probability of winning?
L1 / L3 / L4 / L5 / L5P1 / P1, L1 / P1, L3 / P1, L4 / P1, L5 / P1, L5
P2 / P2, L1 / P2, L3 / P2, L4 / P2, L5 / P2, L5
P3 / P3, L1 / P3, L3 / P3, L4 / P3, L5 / P3, L5
P4 / P4, L1 / P4, L3 / P4, L4 / P4, L5 / P4, L5
P6 / P6, L1 / P6, L3 / P6, L4 / P6, L5 / P6, L5
Using a tree diagram with Compound Events
EXAMPLE: A bag contains 1 blue (B) and 2 green (G) marbles. Harrison will reach into the bag and pick a marble without looking. Without replacing the first marble, he will pick a second marble without looking. What is the probability that he will pick a green marble first and a blue marble second?
First, Use 3 branches to show the possible outcomes of Harrison’s first pick.
First Pick
B
G
G
Second, Draw additional branches to show the possible outcomes of his second pick. Since the first marble will not be replaced, the events are dependent.
· If he picks a blue marble first, then he must pick a green marble second.
· If he picks a green marble first, then he can pick either a blue marble or a green marble second.
First Pick Second Pick Outcomes
______
B ______
G ______
______
G ______
______
Third, determine the probability that he will pick a green marble first and a blue marble second. There are ____ favorable outcomes, GB. There are ___ possible outcomes.
What is the probability that Harrison will pick a green marble first and a blue marble second? ______
**Suppose Harrison will replace the first marble before picking the second marble. How would that change the probability described above?
Name: ______Date: ______Period: ____
MCC7.SP.8: Probabilities of Compound Events
Compound Event: a combination of two or more events in a probability experiment.
Dependent Event: an event in which the first outcome affects the second outcome.
Independent Event: an event in which the first outcome does not affect the second outcome.
Tree Diagram: a representation that uses branches to show all the possible outcomes for a probability experiment.
EXAMPLE: Using a table with Compound Events
If I toss two fair coins at the same time, is the probability that both coins will land on heads ½?
First, use the table to find the sample space for tossing two coins at the same time.
Heads (H) / Tails (T)Heads (H) / HH / HT
Tails (T) / TH / TT
Second, find out how many possible outcomes are in the sample space. ___4______
Third, Circle the outcomes that show both coins landing on heads.
Fourth, determine how many favorable outcomes there are. __1_____
Finally, determine the probability of both coins landing on heads.
____1/4 ____
EXAMPLE: Using a tree diagram with Compound Events
A bag contains 1 blue (B) and 2 green (G) marbles. Harrison will reach into the bag and pick a marble without looking. Without replacing the first marble, he will pick a second marble without looking. What is the probability that he will pick a green marble first and a blue marble second?
First, Use 3 branches to show the possible outcomes of Harrison’s first pick.
First Pick
B
G
B
Second, Draw additional branches to show the possible outcomes of his second pick. Since the first marble will not be replaced, the events are dependent.
· If he picks a blue marble first, then he must pick a green marble second.
· If he picks a green marble first, then he can pick either a blue marble or a green marble second.
First Pick Second Pick Outcomes
G BG
B G BG
G B GB
G GG
G B GB
G GG
Third, determine the probability that he will pick a green marble first and a blue marble second. There are 2 favorable outcomes, GB. There are 6 possible outcomes.
What is the probability that Harrison will pick a green marble first and a blue marble second? _____2/6 OR 1/3______
**Suppose Harrison will replace the first marble before picking the second marble. How would that change the probability described above?