Exam 11: Probability Basics

Use the following Consider rolling a fair six-sided die. Round all answers to three decimal places. -What is the probability that the result is not a 5?

Use the following A bag of peanut butter M&M's contains 188 candies. Of the candies, 28 are blue, 40 are brown, 38 are green, 25 are orange, 34 are red, and 23 are yellow. They are thoroughly mixed up so that each is equally likely to be selected if we pick one. Round all of your answers to four decimal places. -If we select one at random, then put it back, mix them up well (so the selections are independent) and select another one, what is the probability that both the first and second M&M's are blue?

Use the following Consider rolling a fair six-sided die. Round all answers to three decimal places. -What is the probability that the result of rolling the die is a 3?

Use the following Let A and B be two events such that P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.1575. Use two decimal places in your answer unless otherwise specified. -Find P(B if A).

Use the following About 80% of people have seen television ads for a certain product. Of the individuals who see the ad, only 1% buy the product. Of the individuals who do not see the ad, 0.5% buy the product. Round all answers to three decimal places. -Suppose we randomly select an individual and discover that they have bought the product. What is the probability that they have seen the product's advertisement?

Use the following According to a 2006 study described in the New York Times (October 18, 2006), blue eyes are becoming rarer among Americans with only about 17% of Americans having blue eyes. Consider taking a random sample of 50 Americans. Let X represent the number of individuals with blue eyes in the sample. Round all values to three decimal places unless otherwise specified. -What is the probability that 5 or fewer people have blue eyes?

Use the following Determine whether the process describes a binomial random variable. If it is binomial, give values for n and p. If it is not binomial, state why not. -In American Football, when the place kicker attempts a field goal, they are typically more likely to make "short" field goals (when they are kicking relatively close to the end zone) than "long" field goals (when they are relatively far away from the end zone). Suppose a certain place kicker attempts 35 field goals in a season (at different distances) and the number of field goals he made is recorded.

Use the following Identify whether or not each of the following is a valid probability function. If it is not, explain why not. -

Use the following In 2008, the Detroit Lions set an NFL record by losing all 16 regular season games. Suppose that the Lions actually had a 10% chance of winning an individual game in the 2008 season and that each game was independent. Let X represent the number of wins out of 16 regular season games. Round all answers to three decimal places unless otherwise specified. -What is the probability of winning fewer than 4 games?

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Compute the standard deviation of the random variable X.

Use the following Use the provided tree diagram to find the requested probabilities. Round all answers to three decimal places. -P(X if B)

Use the following There are three roofing companies that service a small community. Al's Roof Repair gets 45% of the roofing jobs in the community while Bob's Better Building and Carl's Roof Service get 25% and 30% of the business, respectively. Of Al's customers, 70% are satisfied. Of Bob's customers, 95% are satisfied. Among Carl's customers, 90% are satisfied. Round all answers to four decimal places. -What proportion of roofing customers are satisfied?

Use the following In American Football, a coach on the sideline "calls" a play - either a running play or a passing play. Occasionally, for various reasons, the quarterback may decide to change the play (called an "audible"). Suppose that for a particular team, the coach calls running plays 40% of the time (and thus calls passing plays 60% of the time). When the coach calls a running play, a running play is executed on the field 88% of the time. When the coach calls a passing play, a running play is executed on the field 7% of the time. Round all answers to three decimal places. -Suppose we observe a pass on a randomly selected play. What is the probability that the coach actually called a running play?

Use the following In the classic dice game Yahtzee, players roll five dice and score points by obtaining different combinations of values. Consider rolling five fair dice. Let X represent the number of sixes in a single roll of the five dice. Unless otherwise specified, round all answers to three decimal places. -What is the probability of getting exactly 2 sixes?

Use the following For two events A and B, we have P(A) =0.47, P(B) = 0.33, and P(A and B) = 0.20. -Find P(not A). Use two decimal places.

Use the following According to a 2006 study described in the New York Times (October 18, 2006), blue eyes are becoming rarer among Americans with only about 17% of Americans having blue eyes. Consider taking a random sample of 50 Americans. Let X represent the number of individuals with blue eyes in the sample. Round all values to three decimal places unless otherwise specified. -Explain why X is a binomial random variable.

Use the following In American Football, a coach on the sideline "calls" a play - either a running play or a passing play. Occasionally, for various reasons, the quarterback may decide to change the play (called an "audible"). Suppose that for a particular team, the coach calls running plays 40% of the time (and thus calls passing plays 60% of the time). When the coach calls a running play, a running play is executed on the field 88% of the time. When the coach calls a passing play, a running play is executed on the field 7% of the time. Round all answers to three decimal places. -Suppose we observe a run on a randomly selected play. What is the probability that the coach actually called a passing play?

Use the following A local organization is holding a raffle. There are four prizes: $50, $30, $20, and $10. They have sold 250 tickets. To select the winners, they draw four tickets at random. Let X represent the amount won with a single ticket. Round all answers to two decimal places. -Compute the mean winnings of a single ticket.

Use the following A statistician used a computer to generate 4 random values between 0 and 9. Let X represent the number of these values that are 5 or larger. Round all probability calculations to three decimal places. -Find the mean of the random variable X.

Use the following Determine whether the process describes a binomial random variable. If it is binomial, give values for n and p. If it is not binomial, state why not. -The proportion of babies that are boys is about 0.51. In a kindergarten class with 28 children, count the number of boys. We assume that the sex of each child is independent of the others.