By Kault

ISBN-10: 0313322090

ISBN-13: 9780313322099

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Additional resources for Statistics with Commonsense: Using Statistics with Commonsense

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6. Venn Diagram Conventions Traditionally, Venn diagrams are drawn with ellipses rather than drawn with rectangles. Basic Probability 37 However, the use of rectangles rather than the traditional ellipses shows whether the area of overlap is in proportion to the area of both rectangles, as should be the case for independent events. MORE COMPLICATED PROBABILITY RULES The Modified Addition Rule Often we want to find the probability of a combination of events that do not meet the criteria for the addition rule or the multiplication rule.

This is roughly represented by the Venn diagram. Here the area A (including the area A&B) is about 50 percent of the total area of the Venn diagram rectangle. The area B (including the area A&B) is about 30 percent of the total area of the rectangle. The area A&B itself is about 20 percent of the total area. We see that the sum of all the shaded areas representing the options of A or B or both is about 60 percent of the total area. The Modified Multiplication Rule The modified multiplication rule when events are not independent can be explained by reference to the same diagram.

With equal widths, areas and heights are proportional and we can think of the histogram as representing numbers by height. However, in unusual cases we may want histograms where the interval widths are unequal. For example, say we had the information that of 2,000 newborns who died, 1,000 did so within twenty-four hours of birth and the remaining 1,000 died between twenty-four hours and thirty-one days. The death rate per day after twenty-four hours is one-thirtieth the death rate in the first twenty-four hours.