Exam 5: Discrete Probability Distributions

There are 27,307 undergraduate students enrolled at a certain university. The age distribution is as follows: Age Range Number 13-14 3 15-17 34 18-22 11,450 23-30 9488 31 and up 6332 Total 27,307 What is the probability that a student is between 23 and 30 years old?

A coin is tossed 475 times and comes up heads 242 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500 likely voters, 210 said they planned to write in an independent candidate rather than vote for the Democrat or Republican candidate for mayor. What is the probability that a surveyed voter plans to write in an independent candidate?

A Karate club consists of 35 persons holding a black belt (highest rating), 64 persons holding a brown belt (middle rating), and 97 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a black belt?

The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 166 times and comes up "A" 96 times. Use the Empirical Rule to approximate the probability that the spinner comes up "A".

According to a survey, 68% of teenagers could recognize a picture of legendary film star John Wayne. What is the probability that a randomly-selected teenager could recognize John Wayne?

Evaluate the permutation: $10 {P _ { 4 } }$

A fast-food restaurant chain has 623 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 623 to test market a new menu Given that the outlet is located in a city with a population under 50,000, what is the probability that it is in the Southwest?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space first.]

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are unlocked. List the outcomes of C. [Let "L" designate "locked" and U" designate "unlocked".]

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. Response Number Very satisfied 608 Somewhat satisfied 3376 Dissatisfied 6194 Total 10,178 Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person is dissatisfied with government's spending?

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of C. [Let "L" designate "locked" and U" designate "unlocked".]

On a recent Saturday, a total of 1100 people visited a local library. Of these people, 260 were under age 10, 496 were aged 10–18, 180 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is less than 19 y

The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "A" is drawn first and "B" is drawn second?

A committee consists of 10 women and 7 men. Three members are chosen as officers. What is the probability that all three officers are women?

A survey asked 33,703 homeowners how many pets they owned. The results were as follow Number of Pets Number of Homeowners 0 6705 1 10,544 2 9049 3 6463 4 or more 942 Total 33,703 What is the probability that a sampled homeowner has three pets?

For the event described below, which of the following represents the complement of the event. A sample of 301 software DVDs was selected. At least 34 of these were defective.

A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(B and A) .

In a recent semester at a local university, 540 students enrolled in both General Chemistry and Calculus I. Of these students, 72 received an A in general chemistry, 65 received an A in calculus, and 31 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student did not receive an A in general chemistry.

An unfair coin has a probability 0.4 of landing heads. The coin is tossed two times. What is the probability that it lands heads at least once?