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Block: _______ Date: __________________________________

Two-Way Tables and Independence

The following two-way table is adapted from aggregated national data reported by the Washington Post (2010) regarding race and marijuana use for 75,300 people.

# of people who use marijuana | # of people who do not use | Total | |

White | 20790 | 42210 | 63000 |

Black | 3075 | 9225 | 12300 |

Total | 23865 | 51435 | 75300 |

Using this data, calculate the following probabilities:

- What is the probability that a randomly selected individual uses marijuana?

- What is the probability that a randomly selected white person uses marijuana?

- What is the probability that a randomly selected black person uses marijuana?

- What relationship does there seem to be between race and marijuana use based on this data and your calculations?

The following two-way table is adapted from the same national data reported by the Washington Post. The table illustrates arrests related to marijuana use as reported on the table on the previous page.

# of Arrested | # of non-Arrests | Total | |

Black Marijuana Users | 22 | 3053 | 3075 |

White Marijuana Users | 42 | 20748 | 20790 |

Total | 64 | 23801 | 23865 |

Using this data, calculate the probabilities below – round to three decimal places.

- What is the probability that a randomly selected marijuana user is arrested?

- What is the probability that a randomly selected white marijuana user is arrested?

- Are the “events” of being white and being arrested independent or dependent? If dependent, did this increase or decrease the chance of being arrested?

- What is the probability that a randomly selected black marijuana user is arrested?

- Are the “events” of being black and being arrested independent or dependent? If dependent, did this increase or decrease the chance of being arrested?

- What implications does this data have about our society? Who would be interested in collecting this data? How might different groups react to this data? We’ll discuss this as a class, but start thinking about it!