1. Warm up: Solve each system (any method)

2. W-up 11/4 1) Cars are being produced by two factories, factory 1 produces twice as many cars (better management) than factory 2 in a given time. Factory 1 is know to produce 2% defectives and factory 2 produces 1% defectives. A car is examined and found to be defective, what is the probability it was produced by factory 1? 2. evaluate b(7,4;.20) 3. A fair coin is tossed 8 times, what is the probability of obtaining at least 6 heads? Answers: 1. 80% 2. 2.87% 3. 14.45%

3. 8.3 EXPECTED VALUE SWBAT compute expected values in addition to solving application problems involving expected value.

4. Consider a coin flipping game: If heads shows, you lose $1. If tails shows, you win $2.

5. Expected Value:

6. Steps to compute E: Partition “S” into the “A” events. Determine the probability of each event (Sum of probabilities should = 1). Assign payoff values “m”. Calculate.

7. Compute the expected value: Outcome Probability1/31/61/4 Payoff104-2

8. A player rolls a die and receives the # of $ = to the # of dots on the die. What is the expected value to play? Roll#1#2#3#4#5#6 Probability1/6 Payoff$1$2$3$4$5$6 If E = 0 then the “game” is fair

9. A lab contains 10 microscopes, 2 are defective. If 4 are chosen what is the Expected value of Defective?

10. Assign payoffs of 0 (no defective)1,2 since we are determining the expected #:

11. Expected Value of Bernoulli Trials: With “n” trials the expected # of successes is: E=np *Where “p” is the probability of successes on any single trial.

12. MC Test contains 100 questions each w/ 4 choices. What is the expected # of correct guesses?

13. HW WS: 8.3; #s 1-17odd,21, 25, 27