Exam 4: Probability and Counting Rules

A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?

A furniture manufacturer offers bookcases in 3 different sizes and 4 different colors. If every color is available in every size, then the total number of different bookcases is

In a fish tank, there are 23 goldfish, 4 angelfish, and 9 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy.

A certain system has two components. There are 9 different models of the first component and 12 different models of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different sets of components can the salesman take?

Find the probability of getting a number greater than 4 when a die is rolled one time.

On an eight-question true-false quiz, a student guesses each answer. What is the probability that the student gets at least one of the answers correct?

In a second grade class containing 12 girls and 9 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls?

The Statistics Club at Woodvale College sold college T-shirts as a fundraiser. The results of the sale are shown below. Choose one student at random. Find the probability that the student sold 11-15 T-shirts or less than 6 T-shirts.

A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of ____________ probability.

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?

A club has 10 members. There are 720 ways that a chairperson, a secretary, and a treasurer can be selected from these 10 members. Assume a person can hold, at most, one office.

What is the set of all possible outcomes of a probability experiment?

The ______________ probability of an event B in relationship to an event A is defined as the probability that event B occurs after event A has already occurred.

An apartment building has the following distribution of apartments: If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor?

Given eight students, three of which are female, if two students are selected at random, without replacement, what is the probability that both students are female?

If a menu has a choice of 4 appetizers, 4 main courses, and 4 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert ?

When a die is rolled twice, there are __________ possible outcomes.

In a recent study, the following responses were obtained to the question, "Do you favor recycling in your neighborhood?" If a response is picked at random, what is the probability that it came from a male or that it indicated no opinion regarding recycling?

In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 35% of the residents play poker, and 10% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident plays poker, given that they also garden.

FizzFizz soda comes in two varieties, regular and diet. If a researcher has 4 boxes of each, how many ways can he select 2 boxes of each for a quality control test?