Three of the Most Common Pets Are Cats, Dogs, and Fish

question 12

Essay

Three of the most common pets are cats, dogs, and fish. Many families have more
than one type of pet, and some have all three! Define the following events, with the
probabilities given. (The fish-and-cats combination doesn't seem too popular!) $$\begin{array} { l l } \mathrm { F } = \text { a randomly selected family has at least one pet fish: } & \mathrm { P } ( \mathrm { F } ) = 0.20 \\\mathrm { D } = \text { a randomly selected family has at least one pet dog: } & \mathrm { P } ( \mathrm { D } ) = 0.32 \\\mathrm { C } = \text { a randomly selected family has at least one pet cat: } & \mathrm { P } ( \mathrm { C } ) = 0.35\end{array}$$
Also
$$P ( F \cap D ) = 0.18 ; \quad P ( F \cap C ) = 0.07 ; \quad P ( D \mid C ) = 0.30$$
Suppose that a family is selected at random. Calculate each of the following (show your work):
a) $P ( F \mid D )$
b) $P ( F \cup D )$
c) $P ( C \cap D )$

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