The distribution of colors of candies in a bag is as follows.

If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is a 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?

If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. If you buy one ticket each month for five months, what is the probability that you will win at least one prize?

An experiment has three mutually exclusive outcomes, A, B, and C. If P(A)=0.12, P(B)=0.61, and P(C)=0.27, which of the following must be true?

I. A and C are independent.

II. P(A and B) = 0

III. P(B or C) = P(B) + P(C)