Chapter 7 Sets Probability

1. Chapter 7Sets & Probability Section 7.5 Conditional Probability; Independent Events

2. Lie detectors are not admitted as evidence in courtroom trials due to the fact they are not 100% reliable. An experiment was conducted in which a group of suspects was instructed to lie or tell the truth to a set of questions, and a group of polygraph experts, along with the polygraph (lie detector), judged whether the suspect was telling the truth or not. The results are tabulated below.

3. Estimate the probability that: a.) there will be a miscarriage of justice. 18 / 200 = .09 b.) a suspect is a liar and gets away with the lie. 11 / 200 = .055 c.) the experts� judgment is correct. 182 / 200 = .91

4. Estimate the probability that: d.) a suspect is telling the truth 100 / 200 = .5 e.) a suspect is found to be honest 104 / 200 = .52 f.) a suspect who is telling the truth is found to be honest by the experts. 93 / 100 = .93

5. Conditional Probability A probability problem in which the sample space is reduced by known, or given, information is called a conditional probability. In other words, a conditional probability exists when the sample space has been limited to only those outcomes that fulfill a certain condition.

6. In a newspaper poll concerning violence on television, 600 people were asked, �What is your opinion of the amount of violence on prime-time television � is there too much violence on television?� Their responses are indicated in the table below.

9. A single die is rolled. Find the probabilities of the given events. a.) rolling a 5 b.) rolling a 5, given that the number rolled is odd c.) rolling an odd number, given that a 5 was rolled

10. A pair of dice is rolled. Find the probabilities of the given events. a.) sum is 10 b.) sum is 10, given the sum is even c.) sum is 7, given the sum is odd d.) sum is even, given the sum is 8

11. Product Rule of Probability

12. Example Two cards are drawn without replacement from a standard deck of 52 cards. a.) Find the probability of getting a King followed by an Ace. b.) Find the probability of drawing a 7 and a Jack. c.) Find the probability of drawing two Aces.

19. Independent Events Two events are independent if the probability of one event does not depend / affect the probability (or occurrence) of the other event.

20. Product Rule for Independent Events

21. Dependent Events Two events are dependent if the probability of one event does affect the probability (or likelihood of occurrence) of the other event. Two events E and F are dependent if P(E | F) ? P(E) or P(F | E) ? P(F)

22. Use your own personal experience or probabilities to determine whether the following events E and F are mutually exclusive and/or independent. a.) E is the event �being a doctor� and F is the event �being a woman�. b.) E is the event �it�s raining� and F is the event �it�s sunny�. c.) E is the event �being single� and F is the event �being married�. d.) E is the event �having naturally blond hair� and F is the event �having naturally black hair�. e.) If a die is rolled once, and E is the event �getting a 4� and F is the event �getting an odd number�. f.) If a die is rolled once, and E is the event �getting a 4� and F is the event �getting an even number�.