A license plate has 4 letters and then 2 numbers. Letters cannot be repeated but numbers can be repeated. Find the probability that in a randomly selected license plate the word MATH appears.

Dovid takes an exam that he did not study for. The exam has 7 multiple choice questions. The first 5 are T/F. The last 2 have 4 options each. Dovid guesses on every question. Find the probability that he answers all questions correctly.

A box contains marbles: 3 red, 6 blue, 7 yellow, and 4 purple. How many purple marbles should be added so that p(choosing a purple) becomes 0.9?

A candy jar contains only grape, cherry, orange, and lemon candies. In the jar there are twice as many grape candies as cherry candies, and twice as many cherry candies as orange and lemon candies combined. If there are three times as many orange candies as lemon candies, what is the probability that a candy[…]

In a machine, the probability that it breaks down on a given day is .16. Within one week (7 days), find the probability that the machine breaks down at least once.

The probability of winning a chess game is .54. If you play 2 games, what is the probability that you win twice?