A waterborne nonbacterial gastroenteritis outbreak occurred in Colorado as a result of a long-standing filter deficiency and malfunction of a sewage treatment plant. A study was conducted to determine whether the incidence of gastrointestinal disease during the epidemic was related to water consumption (American Water Works Journal, Jan. 1986). A telephone survey of households yielded the accompanying information on daily consumption of 8-ounce glasses of water for a sample of 40 residents who exhibited gastroenteritis symptoms during the epidemic.

a. If the number of respondents with symptoms does not depend on the daily amount of water consumed, assign probabilities to the four categories shown in the table.
b. Use the information, part a, to find the probability of observing the sample result shown in the table.

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Daily Consumption of 8-Ounce Glasses of Water 5 or more Total 1-2 3-4 Number of respondents with symptoms 6 11 13 10 40