Exam 11: Probability Basics

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 seen the product's advertisement?

Use the following Calculate the requested quantity. -5!

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 variance of the number of heads seen in two tosses of a fair coin. Use one decimal place.

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 Professor Plum is the murderer?

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(II if X)

Use the following A random variable X has the following probability function: Round all answers to two decimal places. -Compute the mean 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(A and Y)

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(A or B). Use four 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. -c

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. -Compute the standard deviation of the number of correct picks on a "Take Five" ticket.

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 Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81. -Find P(A and B). Round your answer to four decimal places.

Use the following Calculate the requested quantity. -3!

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 has green eyes?

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. -Find the standard deviation of the random variable X.

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. -Explain why X is a binomial random variable.

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. -Find the mean of the random variable X. Use one decimal place.

Use the following Suppose A and B are independent events with P(A) = 0.21 and P(B) = 0.81. -Find P(B if A). Use two decimal places.

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 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 fewer than 2 sixes?