Warm up Solve each system any method Wup

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Warm up: Solve each system (any method) • •

Warm up: Solve each system (any method) • •

W-up 11/4 • 1) Cars are being produced by two factories, factory 1 produces

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. 87% 3. 14. 45%

8. 3 EXPECTED VALUE SWBAT compute expected values in addition to solving application problems

8. 3 EXPECTED VALUE SWBAT compute expected values in addition to solving application problems involving expected value.

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

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

Expected Value: •

Expected Value: •

Steps to compute E: • Partition “S” into the “A” events. • Determine the

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.

Compute the expected value: Outcome Probability 1/3 1/6 1/4 Payoff 1 0 4 -2

Compute the expected value: Outcome Probability 1/3 1/6 1/4 Payoff 1 0 4 -2 •

A player rolls a die and receives the # of $ = to the

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 Probability 1/6 1/6 1/6 Payoff $1 $2 $3 $4 $5 $6 If E = 0 then the “game” is fair

A lab contains 10 microscopes, 2 are defective. If 4 are chosen what is

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

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

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

Expected Value of Bernoulli Trials: • With “n” trials the expected # of successes

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.

MC Test contains 100 questions each w/ 4 choices. What is the expected #

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

HW WS: 8. 3; #s 1 -17 odd, 21, 25, 27

HW WS: 8. 3; #s 1 -17 odd, 21, 25, 27