Suppose repetitions are not allowed. Randomly pick up a three-digit number that is formed from the six digits: 1,2,3,4,5,7. What is the probability that this number is even?

The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a female.

Three Bananas and three oranges are kept in a box. If two fruits are chosen at random, Find the probability that one is Banana and another one is orange?

The digits 2, 3, 4, 5, 6, 7, and 8 are randomly arranged to form a​ three-digit number. ​ (Digits are not​ repeated.) Find the probability that the number is even and greater than 800.

A ball is chosen at random out of a bowl that contains 3 red balls, 2 green balls, and 1 blue ball, and then a selection is made from the remaining 5 balls. Find the probability that a red ball and a green ball are selected.

Suppose a jar contains 9 red marbles and 37 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Suppose 4 letters from a sign reading "Montreal" fell on the street. A mathematician find the 4 letters and randomly place them back on the sign (each of them on a spot where a letter fell off). What is the probability the sign reads "Montreal"?