Exam 5: Introduction to Probability

Suppose the inside bottom of a box is painted with three colors: one-third of the bottom area is blue, one-sixth is red, and one-half is yellow. If you toss a tiny pebble into the box without aiming, what is the probability the pebble will NOT land on the color blue?

Suppose you toss a pair of dice. What is the probability that the total number of dots appearing is greater than 7?

If a license plate uses a three-digit number followed by three letters of the English alphabet, how many license plates can be made?

There are seven candidates running for the presidential and vice-presidential nomination. How many different ways are there of selecting presidential and vice-presidential candidates from the field?

For a game, the average amount you can expect to win (or lose) per play in the long run can be measured by:

A candy jar has 12 different pieces of candy in it. If you want to select 2 pieces, how many choices do you have?

A shirt company has three designs that can be made with either short or long sleeves. There are six colors available. How many different types of shirts are available?

You are voting in a state election. There are three candidates for governor, five candidates for lieutenant governor, four candidates for the state house of representatives, and two candidates for senator. How many different ways could you fill out the ballot if you vote once for each office?

Seven horses are running in a race. In how many ways can we have first-, second-, and third-place finishers, assuming there are no ties?

If an event can never occur, then the probability of the event is:

The area of the Unites States is 3.79 million square miles, and Alaska covers 0.59 million square miles. Suppose a meteorite falls from the sky and strikes Earth. What is the probability the meteorite strikes Alaska given it strikes the United States?

The _____ of a test is the probability that the test will detect the disease in a person who does have the disease.

The prevalence of a disease in a given population is the percentage of the population that does NOT have the disease.

You are playing a card game using a full deck without jokers. If you select a face card (jack, queen, or king), you win $6; otherwise, you lose $3. What is the expected value for this game?

Bob and Will toss two coins. If both coins come up heads, Bob pays Will $6. Will pays Bob $2 otherwise. What is the expected value of this game for Bob?

The total number of ways to arrange n distinct items without repetition is:

An ice cream parlor sells 10 flavors. If you'd like a bowl with three scoops, each a different flavor, how many choices do you have?

Suppose you randomly choose two cards from a thoroughly shuffled deck. If you do NOT put the first card back in the deck before you draw the second, what is the probability that the first card is club and the second card is a spade?

Two events, A and B, are independent exactly when P(A or B) = P(A) + P(B).

Suppose there are 15 jelly beans in a bowl-3 green, 5 blue, and 7 red. A jelly bean is selected at random. What is the probability the jelly bean is NOT blue?