Numerade

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Wilfredo Molina

Numerade educator

Say you have a biased coin and you associate obtaining a head with the value 0 whereas obtaining a tail has a value of 2. Let X be the sum of the values obtained from tossing the coin three times. (Round your answers to 4 decimal places, if needed.) (a) If the probability of getting heads in a single toss is 0.38, then what is the probability distribution of X? x | 0 | 2 | 4 | 6 P(X = x) | 2 | | | (b) What is P(X < 6)? (c) What is P(1 < X < 5)?

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Abhirup Pal

Numerade educator

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 83%, indicating they have diabetes. If the child does not have diabetes, the probability that the test will be positive is 10%. Suppose 5.0% of all children actually have diabetes. (Round your answer to 3 decimal places, if needed.) (a) What is the probability that a randomly chosen child has diabetes and tested positive? (b) What is the probability that a randomly chosen child tested positive? (c) Given that a test comes up positive, what is the probability the child has diabetes? (d) What is the probability that a randomly chosen child does not have diabetes and tested negative? (e) What is the probability that a randomly chosen child tested negative? (f) Given that a test comes up negative, what is the probability the child does not have diabetes?

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Juan Nicolás

Numerade educator

Recent MLS listings of houses for sale in Edmonton show that 55% have attached garages, 35% have detached garages, and 20% have a home theatre. Additionally, 50% of houses with a home theatre have an attached garage, and 80% 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? Answer: b) What is the probability that a house has an attached garage and a home theatre? Answer: c) What is the probability that a house has an attached garage, but no home theatre? Answer: d) What is the probability that a house has a detached garage, but no home theatre? Answer: e) What is the probability that a house has a garage, but no home theatre? Answer: f) What is the probability that a house has a home theatre given it has an attached garage? Answer:

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Abhirup Pal

Numerade educator

You decide to start taking coins out of your piggy bank. Currently, your piggy bank has 45 coins, of which 12 are toonies and 9 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? (b) What is the probability that at least one of the first two coins you pick is a toonie? (c) What is the probability that the first three coins you pick are all either loonies or toonies?

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Juan Nicolás

Numerade educator

A survey was conducted from a large group of high school students in an effort to determine what science courses they were currently enrolled in. It was found that 60% of the students were enrolled in Chemistry, 66% of students were enrolled in Physics, and 46% of students were enrolled in Biology. Assume independence between the science classes that each student is enrolled in. (a) What is the probability that a randomly selected student is enrolled in Chemistry and Physics, but not Biology? (b) What is the probability that a randomly selected student is enrolled in Physics but not Chemistry? (c) What is the probability that a randomly selected student is enrolled in Chemistry or Biology?

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