Exam 4: A Survey of Probability Concepts

Type of Attack Find the probability that when 1 of the 2000 subjects is randomly selected, the person chosen was robbed or was victimized by an acquaintance or relative.

The customer service department of H&R Block received a total of 235 telephone requests for a tip-sheet on personal tax or corporate tax. The following table summarizes callers' primary area of interest, and how they first heard about the tip-sheet. Suppose that a caller is selected at random. Find the probability that the caller selected is interested in personal tax, if they heard about the report from the radio.

A tire manufacturer truthfully advertises that "the average life of our new all-season radial tire is 100,000 kilometres." You purchase four of these tires. What is the probability that all four tires will wear out before traveling 100,000 kilometres?

A study of 200 stamping firms revealed these incomes after taxes: What is the probability that a particular firm selected has $1 million or more in income after taxes?

You take a trip by air that involves three independent flights. If there is a 90 percent chance each specific leg of the trip is done on time, what is the probability all three flights are late?

A study of the opinion of designers with respect to the primary colour most desirable for use in executive offices showed that: What is the probability that a designer does not prefer yellow?

A tire manufacturer advertises, "the median life of our new all-seasonradial tire is 120,000 km. An immediate adjustment will be made on any tire that does not last 120,000 km." You purchased four of these tires. What is the probability that all four tires will wear out before traveling 120,000 km?

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow. What is the probability of finding a sports car or a compact car?

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow. What is the probability of finding a vehicle that is either a SUV or grey in colour?

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?

An insurance company has collected the following data on the gender and marital status of 400 customers. Suppose that a customer is selected at random. Is it more likely to be a single female or a single male? Determine the probabilities of each.

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. What is the probability of selecting and finding that all three of them are overweight?

Considering the chart below, what is the probability that if you select one person at random that they committed a violent crime, given that they were over 40 years of age?

Information on the 30 Major League Baseball teams for the 2013 season has been summarized based on game attendance. What is the probability that if a team is selected at random, it had a winning season?

Giorgio offers the person who purchases a 250 ml bottle of Allure two free gifts, either an umbrella, a 30 ml bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you selected at random an umbrella and a shaving kit in that order?

A builder has agreed not to erect all "lookalike" homes in a new subdivision. Five exterior designs are offered to potential homebuyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways are the exterior and interior plans offered to potential homebuyers?

The machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim approached the machine first. They both said they wanted red gum balls. What is the likelihood they will get their wish?

(i. If there is absolutely no chance a person will purchase a new car this year, the probability assigned to this event is zero. (ii) If the set of events are collectively exhaustive and mutually exclusive, the sum of the probabilities equals 1. (iii) Suppose four heads did appear face up on the toss of a coin four times. The probability that a head will appear face up in the next toss of the coin is 1/2 or 0.5.

Each salesperson in a large department store chain is rated with respect to sales potential for advancement. These traits for the 500 salespeople were cross classified into the following table. What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are not permitted, how many different units can be decorated?