Download S.CP.B.8 Assessment Items - Howard County Public School System

Geometry Items to Support Formative Assessment
Unit 5: Probability of Compound Events
Additional GT Standards
Use the rules of probability to compute probabilities of compound events in a uniform
probability model.
S.CP.B.8 (+) Apply the Multiplication Rule in a uniform probability model P(A and
B)=P(A)P(B|A)=P(B)P(A|B), and interpret the answer in terms of the model. (Geometry GT
only)
S.CP.B.8+ Task
Describe two events for which the Multiplication Rule would apply. Explain how you know that
the multiplication rule is applicable.
Answers will vary. The two events should be dependent events.
S.CP.B.8+ Item 1
Examine the spinner below. What is the probability that you land on pink on your first spin and
a number greater than 2 on the second spin? Does the multiplication rule in a uniform
probability model apply? Why or why not?
Solution:
Event A: land on pink on first spin
Event B: land on a number greater than 2 on second spin
1
P(A) =
5
3
P(B) =
5
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
P(A and B) =
1 3 3
× =
5 5 25
The multiplication rule does not apply because the two events are independent.
S.CP.B.8+ Item 2
Mrs. Parker is competing on a game show in which she selects two boxes from a set of twenty.
Fifteen of the boxes contain $50 each and five of the boxes contain $5000 each. What is the
probability that she will select two boxes containing $5000? Does the multiplication rule in a
uniform probability model apply? Why or why not?
Solution: The multiplication rule does apply because the events are dependent. Once a box is
selected, Mrs. Parker will not be selecting the box again.
Event A: The first box selected contains $5000.
Event B: The second box selected contains $5000.
5 1
=
20 4
4
P(B/A) =
19
P(A) =
P(A and B) = P(A) × P(B A) =
1 4
1
× =
4 19 19
So the probability that Mrs. Parker draws two boxes containing $5000 each is
1
.
19
S.CP.B.8+ Item 3: (Open-ended variation)
The following cards have been placed in a bag:
Write a probability question that would require the use of the multiplication rule. Then find the
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.
probability.
Answers will vary. The question should include dependent events (no replacement of the card).
S.CP.B.8+ Item 4:
The following cards have been placed in a bag:
You select a card, do not replace the card in the bag, and then select a second card. If Event A is
“draw a five on the first draw” and Event B is “draw a heart on the second draw”. Find the
probability that both events will occur.
Solution: The multiplication rule does apply because the events are dependent.
2 1
P(A) =
=
12 6
3
P(B|A) =
11
1 3
1
P(A and B) = P(A) × P(B A) = × =
6 11 22
1
So the probability of drawing a 5 and then a heart is
.
22
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.