1) The probability of an event not occurring is equal to 1 minus the probability of it occurring. 2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities. 3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.

1. 11.6 Probabilities Involving NOT and OR

2. Problem 1 Imagine throwing a die. What is the probability of getting a 2? What is the probability of not getting a 2?

3. Probability of an Event NOT occurring (a.k.a. P (NOT) ) The probability that an event E will not occur is equal to 1 minus the probability that it will occur P (not E) = 1 – P (E)

4. Sample Problems (# 2) If you throw a die, what is the probability of not getting an even number? If you are dealt one card from a standard 52-deck card, what is the probability of not getting A king? A heart? A picture card?

5. Problem # 3 Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. Find the probability of not getting a 2 Find the probability of not getting an odd number

6. ODDS Odds in favor of an event = P (E) P (not E) Odds against E = P (not E) P (E) Note: Odds in favor and odds against are reciprocals.

7. Sample Problems (#4) In a standard 52-deck card, Find the odds in favor of getting a king Find the odds against getting a diamond Find the odds in favor of getting a black ace Find the odds against getting a red picture card

8. Sample Problems (# 5) If you toss 2 coins together, the possible outcomes are {HH, HT, TH, TT} Find the odds in favor of getting two heads Find the odds against getting a head and a tail.

9. Odds to Probability If the odds in favor of event E are a to b, then the probability of the event is P(E) = a a + b Example: The odds in favor of winning a horse winning a race are 2 to 5. What is the probability that the horse will win?

10. Probabilities Involving OR Mutually exclusive events – events that occur simultaneously If A and B are mutually exclusive events, then P(A or B) = P (A) + P(B) Example: In a standard 52-deck card, what is the probability of getting a king or a queen?

11. Sample Problems (# 6) If you roll a single die, what is the probability of getting: 3 or a 5 A number less than 3 or number greater than 4

12. Probabilities Involving OR What if the events are not mutually exclusive? OR Probabilities with events that are not mutually exclusive If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P (A and B) Suppose you’re asked to pick a card from a standard 52-deck card. What is the probability of getting a king or a diamond?

13. Sample Problems (# 7) Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. What is the probability of getting a number greater than 2 or an odd number? What is the probability of getting an odd number or a number less than or equal to 3?

14. Assignment Class work: pages 601-602, #s 5, 9, 15, 23, 33 HW: pages 601-603, #s 2-66 (even)