Exam 11: Probability Basics

Use the following In the game Pass the Pigs, players score (or lose) points by rolling a pair of rubber pigs. The number of points scored depends upon the configuration of the pigs when they land. A paper that appeared in the Journal of Statistics Education (Volume 14, Number 3, 2006) describes a dataset obtained by rolling the pigs many times. The probability function for the number of points scored on a roll (X) is displayed in the following table: Round all answers to two decimal places. -Compute the standard deviation of the number of points scored on a roll.

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 called a running play?

Use the following On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table. Round your answer to each question to three decimal places. -What is the probability that a randomly selected student is a male, if we know that they have hazel eyes?

Use the following About 25.4% of Iowa residents are classified as obese. Suppose we take a random sample of 200 Iowa residents. Let X represent the number of residents that are obese. Round all answers to three decimal places unless otherwise specified. -What is the probability that 49 or 50 people are obese?

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. -Are events A and B disjoint? Explain briefly.

Use the following A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope. Round all answers to three decimal places. -What is the probability that the knife is the murder weapon?

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 B). Use two decimal places.

Use the following The New York Lottery has a daily game called "Take Five" where you win prizes based on how many of the 5 selected numbers match your ticket. The probability function for the number of correct picks on a ticket (X) is displayed in the provided table. Round all answers to three decimal places. -What is the mean number of correct picks on a "Take Five" ticket?

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

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. -What is the probability that 2 or more of the values are 5 or larger?

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 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 not bought the product. What is the probability that they have not seen the product's advertisement?

Use the following Calculate the requested quantity. -

Use the following Let X represent the number of heads seen in two tosses of a fair coin. The probability function for this random variable is summarized in the provided table. Round all answers to two decimal places unless otherwise specified. -Compute the standard deviation of the number of heads seen in two tosses of a fair coin.

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. -Randomly select one adult from each of the 50 U.S. states, and count the number that are obese.

Use the following A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope. Round all answers to three decimal places. -Suppose while playing the game you discover that the rope is the murder weapon. Given this information, what is the probability that Colonel Mustard is the murderer?

Use the following A computer science student is writing a simplified version of the classic murder-mystery game Clue for his class project. In his implementation, there are three equally likely suspects: Miss Scarlet, Colonel Mustard, and Professor Plum. If Miss Scarlet is the murderer, there is a 40% chance she uses the knife, 35% chance she uses the lead pipe, and a 25% chance she uses the rope. If Colonel Mustard is the murderer, there is a 20% chance he uses the knife, a 30% chance he uses the lead pipe, and a 50% chance he uses the rope. If Professor Plum is the murderer, there is a 30% chance he uses the knife, a 40% chance he uses the lead pipe, and a 30% chance he uses the rope. Round all answers to three decimal places. -Suppose while playing the game you discover that the knife is the murder weapon. Given this information, what is the probability that Miss Scarlet is the murderer?

Use the following On the first day of class, students in a large introductory statistics course were asked their sex and eye color. The results are summarized in the provided table. Round your answer to each question to three decimal places. -Are hazel eyes and male disjoint? Explain briefly.

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 standard deviation of the amount won with a single ticket.

Use the following Consider rolling a fair six-sided die. Round all answers to three decimal places. -Suppose we record the result of the roll and then roll the die a second time. What is the probability that both rolls are a 6?