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# 11.6 Probability Involving Or and Not

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### 11.6 Probability Involving Or and Not

1. 1. 11.6 Probabilities Involving NOT and OR<br />
2. 2. Problem 1 <br />Imagine throwing a die. What is the probability of getting a 2?<br />What is the probability of not getting a 2?<br />
3. 3. Probability of an Event NOT occurring (a.k.a. P (NOT) )<br />The probability that an event E will not occur is equal to 1 minus the probability that it will occur<br />P (not E) = 1 – P (E)<br />
4. 4. Sample Problems (# 2)<br />If you throw a die, what is the probability of not getting an even number?<br />If you are dealt one card from a standard 52-deck card, what is the probability of not getting<br />A king?<br />A heart?<br />A picture card?<br />
5. 5. Problem # 3<br /> Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. <br />Find the probability of not getting a 2<br />Find the probability of not getting an odd number<br />
6. 6. ODDS<br />Odds in favor of an event = P (E)<br /> P (not E)<br />Odds against E = P (not E)<br /> P (E)<br />Note: Odds in favor and odds against are reciprocals.<br />
7. 7. Sample Problems (#4)<br />In a standard 52-deck card, <br />Find the odds in favor of getting a king<br />Find the odds against getting a diamond<br />Find the odds in favor of getting a black ace<br />Find the odds against getting a red picture card<br />
8. 8. Sample Problems (# 5)<br />If you toss 2 coins together, the possible outcomes are {HH, HT, TH, TT}<br />Find the odds in favor of getting two heads<br />Find the odds against getting a head and a tail.<br />
9. 9. Odds to Probability<br />If the odds in favor of event E are a to b, then the probability of the event is <br />P(E) = a<br /> a + b<br />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?<br />
10. 10. Probabilities Involving OR<br />Mutually exclusive events – events that occur simultaneously <br />If A and B are mutually exclusive events, then <br /> P(A or B) = P (A) + P(B)<br />Example: In a standard 52-deck card, what is the probability of getting a king or a queen?<br />
11. 11. Sample Problems (# 6)<br />If you roll a single die, what is the probability of getting:<br /> 3 or a 5<br />A number less than 3 or number greater than 4<br />
12. 12. Probabilities Involving OR <br />What if the events are not mutually exclusive?<br />OR Probabilities with events that are not mutually exclusive<br />If A and B are not mutually exclusive, then <br />P(A or B) = P(A) + P(B) – P (A and B)<br />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?<br />
13. 13. Sample Problems (# 7)<br />Assume that it is equally probable that the pointer will land on any one of the five numbered spaces.<br />What is the probability of getting a number greater than 2 or an odd number?<br />What is the probability of getting an odd number or a number less than or equal to 3?<br />
14. 14. Assignment<br />Class work: pages 601-602, #s 5, 9, 15, 23, 33<br />HW: pages 601-603, #s 2-66 (even)<br />