EXAMPLE 15 Union and intersection

Recall from Section 2.1 that a contingency table (also known as a crosstabulation) is a tabular summary of the relationship between two categorical variables. Table 6 contains a contingency table summarizing the gender and survival status of the passengers and crew of RMS Titanic.

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Suppose our experiment is to select one person at random from the passengers and crew. Define the following events:

  1. Find the intersection of these events, ( and ).
  2. Find the union of these events, ( or ).

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Solution

  1. The intersection of and is the event containing the outcomes that are common to both and . Note in Table 6 that the female outcomes form a column and the survived outcomes form a row. The intersection of and lies at the “intersection” of this column and this row, as illustrated in Table 6. The green cell belongs both to the Female column and the Survived row, and thus belongs to both events. The green cell therefore represents the intersection, , which includes the 344 passengers and crew who were both female and survived.
  2. The union of and is the event containing all the people who were either female or who survived, or both. That is, the union contains the following groups:

Thus, in Table 6, the union is represented by the cells containing 126, 344, and 367.

NOW YOU CAN DO

Exercises 13–18.