Exam 11: Probability Basics

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(I if X)

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

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

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 not winning a single game?

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(I if Y)

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

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

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 3 or more 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(B if A). Use three decimal places.

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 Bob's Better Building and is satisfied?

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

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 mean number of points scored on a roll.

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 standard deviation of the typical payout of a "Take Five" ticket.

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 M&M at random, what is the probability that it is not red?

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 M&M at random, what is the probability that it is orange or yellow?

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. -a

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 only 1 or 2 picks correct?

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. -What is the probability that a randomly selected individual has not bought the product?

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 a large bag of M&M's, select 10 candies and count the number of red candies.