1. Discrete Math Section 16.1 Find the sample space and probability of multiple events The probability of an event is determined empirically if it is based on past experiences. The sample space for an event is the set S of all possible outcomes. The probability of an event is determined theoretically if it is based on reasoning alone. Examples of sample spaces Flipping a coin S = (heads, tails) Roll a die S = (1,2,3,4,5,6)

2. The probability of an event A, denoted P(A) is: P(A) = m n where m is the number of desired possibilities and n is the number of possibilities in the sample space. Example: A single die is rolled. What is the sample space? What is the probability of rolling an even number?

3. Probability of either of two events. For events A and B: P(A or B) = P(A) + P(B) – P(A and B) Example: When one die is rolled, what is the probability of obtaining a number that is odd or a number that is prime? Two events that can not both occur are mutually exclusive events Probability of mutually exclusive events: P(A or B) = P(A) + P(B)

4. P(A or not A) = 1 thus, P(not A) = 1 – P(A) Example: You toss a coin four times. a.How many different outcomes are possible? b.Find the probability of obtaining no heads. c. Find the probability of obtaining at least one head. d. Find the probability of obtaining exactly one head. Example: Each of five cards is labeled with a letter A,B,C,D, or E. Two cards are chosen at random without the first card being replaced. a.List all the possible outcomes. b. Find the probability that both letters chosen are consonants.

5. Assignment Page 603 Problems 2,4,5,6,8,10,12,18,22,24,28