Geometry Items to Support Formative Assessment
Unit 5: Probability of Compound Events
Part I: Probability of Compound Events
Understand independence and conditional probability and use them to interpret data.
S.CP.A.2 Understand that two events A and B are independent if the probability of A and B
occurring together is the product of their probabilities, and use this characterization to determine
if they are independent.
S.CP.A.2 Item 1:
This Friday there is a 60% chance of the temperature rising above 95°, a 40% chance of a
thunderstorm, and a 30% chance of both events occurring. Are the events “temperature rising
above 95° on Friday” and “thunderstorm on Friday” independent events? Justify your answer.
Possible Solution:
P(temperature above 95°) = 0.6
P(thunderstorm) = 0.4
P(temperature above 95° and thunderstorm) = 0.3
Since P(temperature above 95°) × P(thunderstorm) = (0.6)(0.4) = 0.24
Since 0.24 ¹ 0.3, the two events are not independent.
S.CP.A.2 Item 2:
You and your friend are helping each other study for a test on probability. Your friend made up
the following problem for you to solve.
The probability that you are a vampire is 0.23 and the probably that the sun burns your
skin is 0.14. Are the events dependent or independent if the probability that you are a
vampire and the sun burns your skin is 0.0322. Explain your answer.
Solution:
The events are independent. (0.23)(0.14) = 0.0322. Two events are independent if the probability
of them both occurring is the product of the probabilities of each of them occurring.
S.CP.A.2 Item 3:
Ciara, one of your classmates, was absent when the class learned about dependent and
independent events. Since you did so well on the exit ticket that day, your teacher has asked you
to explain this topic to Ciara. What would you tell Ciara? Use P(A) = 0.21 and P(B) = 0.36 in
your explanation.
Solution:
The explanation should include that the events are independent if the probability of events A and
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B occurring together is = (0.21)(0.36) = 0.0693.
S.CP.A.2 Item 4:
The probability that Ari cleaned his room this morning is 15%. The probability that Ari cleaned
his room and his Mom is upset with him is 6%.
What is the probability that Ari’s Mom is upset with him if:
a. Ari cleaning his room is independent of his Mom being upset with him? Explain your answer.
b. Ari cleaning his room is dependent on his Mom being upset with him? Explain your answer.
c. Do you think these events are more likely to be independent or dependent? Explain your
answer.
Solution:
a. 40%. If the events are independent then the product of each events probability equals the
probability of the events occurring together. (0.15)(0.4)=0.06.
b. any % that is not 40. If the events are dependent then the product of each events probability
does not equal the probability of the events occurring together.
c. I think these events are more likely to be dependent, because the cleanliness of Ari’s room will
likely affect his mom’s mood.
S.CP.A.2 Task:
A recent poll found that 56% of cell phone users have smartphones. Below is a graph of the
breakdown of the types of smartphones that are being used.
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William uses the following math to justify that owning a smartphone and owning an Android are
independent events.
(0.56)(0.28) = 0.1568.
Do you agree with his justification? If not, explain the misconception behind his work.
Possible Solution:
William’s justification is incorrect because owning an Android is a subset of owning a
smartphone. These are not unique events, and therefore they cannot be independent.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.