Exam 11: Probability Basics

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

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. -The highest point outcome in the game, called a "Yahtzee," occurs when all five dice display the same value. What is the probability of getting exactly 5 sixes? Round your answer to five decimal places.

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

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

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 does not have 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. -What is the probability that more than 15 pitches are strikes?

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. -Explain why X is a binomial random variable.

Use the following Consider rolling a fair six-sided die. Round all answers to three decimal places. -What is the probability that the result is a 2 or a 4?

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 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(X)

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

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

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. -Use the provided information to create a tree diagram.

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

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 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. -Use the provided information to construct a tree diagram.

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 brown?

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 running play occurs on a randomly selected play?

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.