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] AL1 (9-12) 47 :

[MA2015] AL2 (9-12) 40 :

[MA2015] AL2 (9-12) 42 :

[MA2015] AL2 (9-12) 43 :

[MA2015] PRE (9-12) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 49 :

[MA2015] ALT (9-12) 44 :

[MA2015] ALT (9-12) 46 :

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 ) 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] PRE (9-12) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 49 :

49 ) Evaluate reports based on data. [S-IC6]

[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]

[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]

Learn about the origins and meaning of “p-value,” a statistical measure of the probability that has become a benchmark for success in experimental science, in this video from NOVA: *Prediction by the Numbers*. In the 1920s and 1930s, British scientist Ronald A. Fisher laid out guidelines for designing experiments using statistics and probability to judge results. He proposed that if experimental results were due to chance alone, they would occur less than 5 percent (0.05) of the time. The lower the p-value, the less likely the experimental results were caused by chance. Use this resource to stimulate thinking and questions about the use of statistics and probability to test hypotheses and evaluate experimental results.