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Recent MLS listings of houses for sale in Edmonton show that 45% have attached garages, 15% have detached garages, and 26% have a home theatre.

Recent MLS listings of houses for sale in Edmonton show that 45% have attached garages, 15% have detached garages, and 26% have a home theatre. Additionally, 64% of houses with a home theatre have an attached garage, and 82% of houses with a detached garage do not have a home theatre. (Round your answers to 3 decimal places, if needed.)

a) What is the probability that a randomly chosen house has a garage?

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b) What is the probability that a house has an attached garage and a home theatre?

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c) What is the probability that a house has an attached garage, but no home theatre?

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d) What is the probability that a house has a detached garage, but no home theatre?

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e) What is the probability that a house has a garage, but no home theatre?

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f) What is the probability that a house has a home theatre given it has an attached garage?

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