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Exam 4: Probability and Probability Distributions

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Question 61

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The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

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Question 62

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Studies have shown a particular television commercial is understood by 25% of first grade students and 80% of fourth grade students. If a television advertising agency randomly selects one first grader and one fourth grader, what is the probability neither child would understand the commercial, assuming the children's reactions are independent? ______________

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Question 63

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Which of the following statements is correct?

The time required to assemble a computer is an example of a discrete random variable.

Heidi prepares for an exam by studying a list of 15 problems. She can solve nine of them. For the exam, the instructor selects seven questions at random from the list of fifteen. What is the probability that Heidi can solve all seven problems on the exam? ______________

Let x denote the weight gain in pounds per month for a calf. The probability distribution of x is shown below. a. Find the average weight gain in pounds per month for a calf. ______________ b. Find the variance of the weight gain. ______________ c. What is ? ______________ d. What is ? ______________ e. What is ? ______________

If P(A) > 0, P(B) > 0, and P(A B) = 0, then the events A and B are independent.

Which of the following correctly describes experiments?

Which of the following best describes the concept of marginal probability?

Which of the following statements if false?

If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.20, then the events A and B are mutually exclusive.

An interior decorator must furnish two offices. Each office must have a desk, a chair, a file cabinet and 2 bookcases. At a local office furniture store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases, all of which are compatible. (Any desk can be matched with any chair, etc.) How many choices does the decorator have if he wants to select two desks, two chairs, two file cabinets and four bookcases if he doesn't want to select more than one of any model? ______________

If an investor was interested in assessing the probability that a new supermarket will be successful in a New York market area, he would most likely use the relative frequency definition of probability as the method for assessing the probability of success.

In general, the simple events of an experiment take on values between 0 and 1.0, inclusive.

A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below. a. What is the probability that no sales are made? ______________ b. What is the probability that at least one sale is made? ______________ c. What is the probability that exactly one sale is made? ______________ d. What is the probability that exactly two sales were made? ______________

The possible number of combinations of 3 out of 8 distinct items equals:

A manufacturing firm producing odd-sized, decorative windows buys the window frames from either supplier S₁ or supplier S₂. The firm sells the finished window to either customer C₁ or customer C₂. a. Describe the sample space; that is, list all possible supplier-customer combinations, which a given finished window might represent. __________________________________________ b. If each supplier-customer combination in part (a) is equally likely, what is the probability a randomly chosen finished window is sold to customer C₁? ______________

If A and B are two independent events with P(A) = 0.25 and P(B) = 0.45, then P(A B) = 0.70.

A businessman in Chicago is preparing an itinerary for a visit to five major cities. Each city will be visited once and only once. The distance traveled, and hence the cost of the trip, will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible? ______________

Steve takes either a bus or the subway to go to work with probabilities 0.25 and 0.75, respectively. When he takes the bus, he is late 40% of the days. When he takes the subway, he is late 30% of the days. If Steve is late for work on a particular day, what is the probability that he took the bus? ______________