Exam 11: Probability Basics

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 rope is the murder weapon?

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. -Find the mean number of sixes in a roll of five fair dice.

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

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. -If a randomly selected customer is dissatisfied, what is the probability they used Bob's Better Building?

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 lead pipe is the murder weapon. Given this information, what is the probability that Colonel Mustard 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. -What is the probability that a randomly selected student in the class is a female or has brown 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. -Explain why X is a binomial random variable.

Use the following When a certain pitcher throws his fastball, 75% of the time it is a strike. Suppose he throws 20 fastballs and that the pitches are independent of one another. Let X represent the number of strikes in 20 pitches. Round all answers to three decimal places. -Explain why X is a binomial random variable.

Use the following A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places. -d

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. -Find P(X = 0).

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 variance of the amount won with a single ticket.

Use the following A partial tree diagram is provided. The missing probabilities are indicated by lower case letters. For each of the following, find the indicated probability. Round all answers to three decimal places. -P(Y)

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, keep it, and then select a second one, what is the probability that the first one is yellow and the second one is blue?

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. -Toss a fair coin until it lands heads three times. Count the number of tosses required.

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 3 of the values are 5 or larger?

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. -If a randomly selected customer is dissatisfied, what is the probability that they used Al's Roof Repair?

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 in the class is a female and has hazel eyes?

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 exactly 5 people in the sample have blue eyes?

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 called a passing play?

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 typical payout on a ticket (X) is displayed in the provided table. Round all answers to two decimal places. -Compute the mean typical payout of a "Take Five" ticket.