# Access Point #: MAFS.912.S-CP.1.AP.3b

Identify when two events are independent. P(A and B) ÷ P(A) = P(B)
Clarifications:

#### Essential Understandings

Concrete:

• Use two different manipulatives (e.g., spinner, dice and coins) to demonstrate how events are generated (flipping a coin and rolling a die).
• Use pictures (e.g., picture of the coin, picture of die) to record two different events (results).
• Create a chart of all possible event combinations to determine the probability of a specific event.
Representation:
• List the possible events (results) from two different manipulatives (e.g., die: 1, 2, 3, 4, 5, 6 coin: head, tail).
• Use the list of possible events to show how one event does not affect the other.
• Understand the concept of independent as two events that generate results without affecting each other.
• Represent the probability of each event using numbers. E.g., P(heads) = 1/2 is the probability of flipping a coin and getting heads; P(2) = 1/6 is the probability of rolling a die and getting a 2.
• Multiply the probability of two events together. E.g., P(heads) = 1/2, P(2) = 1/6; P(heads and 2) = 1/2 × 1/6 = 1/12
• Divide the probability of two events together by the probability that one of those events will happen.
• E.g., P(heads) = 1/2, P(2) = 1/6; P(heads and 2) = 1/2 × 1/6 = 1/12
• P(heads and 2) ÷ P(2) = 1/12 ÷ 1/6 = 1/2
General Information
Number: MAFS.912.S-CP.1.AP.3b
Category: Access Points
Cluster: Understand independence and conditional probability and use them to interpret data. (Algebra 2 - Additional Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

## Related Standards

This access point is an alternate version of the following benchmark(s).

## Related Courses

This access point is part of these courses.
1200330: Algebra 2
1200340: Algebra 2 Honors
1210300: Probability and Statistics Honors
1200335: Algebra 2 for Credit Recovery
7912095: Access Algebra 2

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