Exam 11: Probability Basics

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. -Players of the "Take Five" game receive a prize for getting two or more picks correct. What is the probability of getting a prize?

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Find P(X is even).

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. -It is believed that 10% of people are left handed. Randomly sample 100 adults, and count the number that are left handed.

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(III if Y)

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. -Construct a table to display the probability function of this random variable.

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 brown and blue eyes disjoint? Explain briefly.

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

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Find P(X < 2).

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 Professor Plum 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 has blue eyes if we know they are female?

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 probability of getting fewer than 3 picks correct?

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 is the probability that a randomly selected customer used Al's Roof Repair and is dissatisfied?

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 the murderer is Miss Scarlet?

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

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. -What is the probability that a passing play occurs on a randomly selected play?

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(A or B). Use two decimal places.

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 mean number of heads seen in two tosses of a fair coin.

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 satisfied, what is the probability that they used Al's Roof Repair?

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(A if B). Use three decimal places.

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. -b