Reporting Statistics and Probability Category Standard Conditional Probability & the Rules of Probability Benchmark MACC.912.S-CP.1.5 Number Benchmark Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For 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. Also Assesses MACC.912.S-CP.1.3 & MACC.912.S-CP.1.4 or Assessed by Item Types This benchmark will be assessed using MC and FR items. Content Limit to real world contexts and age appropriate situations. Limits Benchmark Students will determine probable outcomes of events using the multiplication Clarification rule. Stimulus Test items may include illustrations of the following: tables, lists, tree Attributes diagrams, and other forms. Response Responses may be in decimal or reduced fraction form. Attributes Sample Item Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose an adult male is randomly selected from a particular population. Assume that the following table shows some probabilities involving the compound event that the individual does or does not smoke and the person is or is not diagnosed with cancer: Event Probability smokes and gets cancer 0.08 smokes and does not get cancer 0.17 does not smoke and gets cancer 0.04 does not smoke and does not get cancer 0.71 Suppose further that the probability that the randomly selected individual is a smoker is 0.25. (a) Find the probability that the individual gets cancer, given that he is a smoker. Answer : 0.08/0.25 = 0.32
Reporting Category Statistics and Probability Standard Conditional Probability & the Rules of Probability Benchmark Number MACC.912.S-CP.1.5 Benchmark Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For 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. Also Assesses or Assessed by MACC.912.S-CP.1.3 & MACC.912.S-CP.1.4 Item Types This benchmark will be assessed using MC and FR items. Content Limits Limit to real world contexts and age appropriate situations. Benchmark Clarification Students will determine probable outcomes of events using the multiplication rule. Stimulus Attributes Test items may include illustrations of the following: tables, lists, tree diagrams, and other forms. Response Attributes Responses may be in decimal or reduced fraction form. Sample Item Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose an adult male is randomly selected from a particular population. Assume that the following table shows some probabilities involving the compound event that the individual does or does not smoke and the person is or is not diagnosed with cancer: Event Probability smokes and gets cancer 0.08 smokes and does not get cancer 0.17 does not smoke and gets cancer 0.04 does not smoke and does not get cancer 0.71 Suppose further that the probability that the randomly selected individual is a smoker is 0.25. (a) Find the probability that the individual gets cancer, given that he is a smoker. Answer : 0.08/0.25 = 0.32
probabilityandstatistics_3.docx