Probability What is the probability of rolling “snake eyes” in one roll? What is the probability of rolling “yahtzee” in one roll?

Probability Rules Any probability is between 0 and 1 0 ≤ P(A) ≤ 1 The sum of the probabilities of all possible outcomes must equal 1 if S is in the sample space, the P(S) = 1 If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities addition rule for disjoint events: P(A or B) = P(A) + P(B) The probability that an event does not occur is 1 minus the probability that the event does occur. complement rule: P(A C ) = 1 – P(A)

Set Notation The set of all outcomes are in either A or B “A union B” “A or B” A  B The set of all outcomes in both A and B “A intersect B” “A and B” A  B The set of no outcomes: empty set  if 2 events are disjoint… A  B = 

Example What is the probability of rolling a 5 with two dice? Using S =  1, 2, 3, 4, 5, 6, 7, 8, 9  –What is the probability of choosing a number greater than 6? –What is the probability of not choosing 1?

Multiplication Rule Two events are independent if knowing that one occurs does not change the probability that the other occurs P(A and B) = P(A)P(B) What is the probability of tossing 5 coins and obtaining all tails?

Independent? Tossing two coins? Dealing two red cards in a row from a standard deck of cards? A doctor measuring your blood pressure twice in a row? Taking an IQ test twice in a row?

Independent or Disjoint The multiplication rule holds if A and B are independent but not otherwise The addition rule holds if A and B are disjoint but not otherwise Disjoint events cannot be independent –If A and B are disjoint, then the fact that A occurs tells us that B cannot occur Independent or Disjoint? –Event A: Randomly selected person is a man –Event B: Randomly selected person is pregnant

Homework 6.2 #37-41, 44, 46-52