 # Standard #: MAFS.912.S-MD.1.3

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Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability: Using Probability to Make Decisions
Cluster: Level 2: Basic Application of Skills & Concepts
Date of Last Rating: 02/14
Status: State Board Approved

#### Related Courses

 Course Number1111 Course Title222 1210300: Probability & Statistics with Applications Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1298310: Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 and beyond (current))

#### Related Access Points

 Access Point Number Access Point Title MAFS.912.S-MD.1.AP.3a Determine the theoretical probability of multistage probability experiments (e.g., draw or select a representation of the theoretical probability for a sample space). MAFS.912.S-MD.1.AP.3b Collect data from multistage probability experiments. MAFS.912.S-MD.1.AP.3c Compare actual results of multi-stage experiment with theoretical probabilities (e.g., make a statement that describes the relationship between the actual results of a multistage experiment with its theoretical probabilities [ex., more, less, same, different, equal]).

#### Lesson Plans

 Name Description Modeling Conditional Probabilities 2 This lesson unit is intended to help you assess how well students understand conditional probability, and, in particular, to help you identify and assist students who have the following difficulties representing events as a subset of a sample space using tables and tree diagrams and understanding when conditional probabilities are equal for particular and general situations. Probability This lesson is designed to develop students' understanding of probability in real life situations. Students will also be introduced to running experiments, experimental probability, and theoretical probability. This lesson provides links to discussions and activities related to probability as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

#### Perspectives Video: Expert

 Name Description History of Probability and the Problem of Points What was the first question that started probability theory? Download the CPALMS Perspectives video student note taking guide.

#### Virtual Manipulatives

 Name Description Interactive Marbles This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet. Plinko Probability The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

#### Worksheet

 Name Description Replacement and Probability This lesson is designed to develop students' understanding of sampling with and without replacement and its effects on the probability of drawing a desired object. The lesson provides links to discussions and activities related to replacement and probability as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons that are designed to be used in succession with the current one.

#### Virtual Manipulatives

 Name Description Interactive Marbles: This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet. Plinko Probability: The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

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