Exam 7: A: Discrete Probability

A die has the numbers 1, 2, 2, 3, 3, 3 on its six sides. If the die is rolled, what is the expected value and variance of the number showing?

you have 40 different books (20 math books, 15 history books, and 5 geography books). -You pick two books at random, one at a time. What is the probability that the two books are from different disciplines?

you pick a bit string from the set of all bit strings of length ten. -What is the probability that the bit string has exactly two 1's?

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random. -Find E(X), where X = the number on the ball you draw.

Three coins are tossed. (a) List the elements in the sample space. (b) Find the probability that exactly two heads show.

What is the probability that the sum of the numbers on two dice is even when they are rolled?

A group of ten women and ten men are in a room. If five of the 20 are selected at random and put in a row for a picture, what is the probability that the five are of the same sex?

you pick a bit string from the set of all bit strings of length ten. -What is the probability that the bit string has more 0's than 1's?

You pick a word at random from the set of all words of length six of letters of the alphabet with no repeated letters. What is the probability that the word has exactly one vowel?

Prove or disprove: $p ( E \cup F ) = p ( E ) + p ( F ) \text { for all events } E \text { and } F$