Suppose 54 of families own a dog say event D 43 of families

Suppose 54% of families own a dog( say, event D), 43% of families own a cat (event C), 14% of families own fish(event F), 20% of families own both a dog and cat, 5% of families own a cat and fish, 5% of families own both a dog and cat, 5% of families own a cat and fish. 5% of families own a dog and fish and 3% of families have all three.

a. What percent of families owned a cat or a dog, but not both? Represent this with an appropriate probability statment (i.e.: P(CnD))and find the value.

b. What percent of families own none of these types of animals? Represent this with an appropriate probability statement(i.e.:P(CnD)) and find the value.

Solution

a)

P[(C U D) n (C n D)\'] = P(C) + P(D) - P(C n D) = 0.54 + 0.43 - 0.20

= 0.77 [answer]

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b)

P[(D U C U F)\'] = 1 - P(D U C U F)

= 1 - [P(D) + P(C) + P(F) - P(D n C) - P(C n F) - P(D n F) + P(D n C n F)]

= 1 - [0.54 + 0.43 + 0.14 - 0.20 - 0.05 - 0.05 + 0.03]

= 0.16 [ANSWER]