You decide to start taking coins out of your piggy bank. Currently, your piggy bank has 40 coins, of which 14 are toonies and 6 are loonies. Suppose that when you take a coin out, you do not put it back in the piggy bank; you are picking coins without replacement. (Round your answers to 4 decimal places, if needed.) (a) What is the probability that the third coin you pick is the first toonie you find?

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(b) What is the probability that at least one of the first two coins you pick is a toonie?

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(c) What is the probability that the first three coins you pick are all either loonies or toonies?

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Recent MLS listings of houses for sale in Edmonton show that 40% have attached garages, 15% have detached garages, and 18% have a home theatre. Additionally, 60% of houses with a home theatre have an attached garage, and 90% of houses with a detached garage do not have a home theatre. (Round your answers to 3 decimal places, if needed.)

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

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

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

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

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Suppose a lab is developing a robust new test to look for diabetes in children. If a child actually has diabetes, the probability that the test will be positive is 84%, indicating they have diabetes. If the child does not have diabetes, the probability that the test will be positive is 12%. Suppose 5.6% of all children actually have diabetes. (Round your answer to 3 decimal places, if needed.)

~ What is the probability that a randomly chosen child has diabetes and tested positive?

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What is the probability that a randomly chosen child tested positive?

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Given that a test comes up positive, what is the probability the child has diabetes?

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What is the probability that a randomly chosen child does not have diabetes and tested negative?

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What is the probability that a randomly chosen child tested negative?

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Given that a test comes up negative, what is the probability the child does not have diabetes?