Classroom Resources (3) |

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 47 :

[MA2015] AL2 (9-12) 40 :

[MA2015] AL2 (9-12) 42 :

[MA2015] AL2 (9-12) 43 :

[MA2015] AL2 (9-12) 38 :

[MA2015] ALT (9-12) 42 :

[MA2015] ALT (9-12) 44 :

[MA2015] ALT (9-12) 46 :

[MA2015] ALT (9-12) 47 :

[MA2015] GEO (9-12) 43 :

47 ) 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-CP2]

[MA2015] AL2 (9-12) 40 :

40 ) Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*. [S-CP3]

[MA2015] AL2 (9-12) 42 :

42 ) Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5]

Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

[MA2015] AL2 (9-12) 43 :

43 ) Find the conditional probability of *A* given *B* as the fraction of *B*'s outcomes that also belong to *A*, and interpret the answer in terms of the model. [S-CP6]

[MA2015] AL2 (9-12) 38 :

38 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] ALT (9-12) 42 :

42 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] ALT (9-12) 44 :

44 ) Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*. [S-CP3]

[MA2015] ALT (9-12) 46 :

46 ) Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5]

Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

[MA2015] ALT (9-12) 47 :

47 ) Find the conditional probability of *A* given *B* as the fraction of *B*'s outcomes that also belong to *A*, and interpret the answer in terms of the model. [S-CP6]

[MA2015] GEO (9-12) 43 :

43 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] (Alabama)

Example:

What is the probability of tossing a penny and having it land in the non-shaded region'

Geometric Probability is the Non-Shaded Area divided by the Total Area.

Explore how probability can be used to help find people lost at sea, even when rescuers have very little information, in this video from NOVA: *Prediction by the Numbers*. To improve its search-and-rescue efforts, the U.S. Coast Guard has developed a system that uses Bayesian inference, a mathematical concept that dates back to the 18th century. The Search and Rescue Optimal Planning System (SAROPS) uses a mathematical approach to calculate probabilities of where a floating person or object might be based on changing ocean currents, wind direction, or other new information. Use this resource to stimulate thinking and questions about appropriate uses of statistical methods.

View Standards
**Standard(s): **
[MA2015] AL2 (9-12) 38 :

[MA2015] ALT (9-12) 42 :

[MA2015] PRE (9-12) 54 :

[MA2015] GEO (9-12) 43 :

38 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] ALT (9-12) 42 :

42 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] PRE (9-12) 54 :

54 ) (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. [S-MD5]

a. Find the expected payoff for a game of chance. [S-MD5a]

Examples: Find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

b. Evaluate and compare strategies on the basis of expected values. [S-MD5b]

Example: Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

[MA2015] GEO (9-12) 43 :

43 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] (Alabama)

Example:

What is the probability of tossing a penny and having it land in the non-shaded region'

Geometric Probability is the Non-Shaded Area divided by the Total Area.

This interactive teaches and provides practice in the identification of odds, the conversion of odds to probabilities and probabilities to odds, and the comparison of odds and probability events. This game is recommended for grades 9 -12.

View Standards
**Standard(s): **
[MA2015] AL2 (9-12) 37 :

[MA2015] AL2 (9-12) 38 :

[MA2015] ALT (9-12) 41 :

[MA2015] ALT (9-12) 42 :

[MA2015] PRE (9-12) 54 :

37 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

[MA2015] AL2 (9-12) 38 :

38 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] ALT (9-12) 41 :

41 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

[MA2015] ALT (9-12) 42 :

42 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7]

[MA2015] PRE (9-12) 54 :

54 ) (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. [S-MD5]

a. Find the expected payoff for a game of chance. [S-MD5a]

Examples: Find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

b. Evaluate and compare strategies on the basis of expected values. [S-MD5b]

Example: Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

Module 5, Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts (S.MD.B.5a, S.MD.B.5b, S.MD.B.6, S.MD.B.7). Students use probabilities to make a fair decision and explain how to make fair an “unfair” decision. Students analyze simple games of chance as they calculate and interpret the expected payoff in context. They make decisions based on expected values in problems with business, medical, and other contexts. They also examine and interpret what it means for a game to be fair. Interpretation and explanations of expected values are important outcomes for Topic C.

**Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.**