Homework: pg. 398 #4, 5 pg. 402 #10, 11 4.) A. A single random digit simulates one shot, 1-7 represents a made shot 8-10 represents a miss. Then 5 consecutive.

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Homework: pg. 398 #4, 5 pg. 402 #10, 11 4.) A. A single random digit simulates one shot, 1-7 represents a made shot 8-10 represents a miss. Then 5 consecutive digits simulates 5 independent shots. B. Approx. 11/50=0.22 (If you use table B) 5.) ANSWERS CAN VARY!!! A. Even #’s: democrat; odd #’s: republican B. 1-6: democrat, 7-10: republican C. 1-4: democrat, 5-8: republican, 9-10: undecided D. 1-53: democrat, 54-100: republican

Homework: pg. 398 #4, 5 pg. 402 #10, 11 10.) A. 1-5: girl; 6-10: boy B. Probabilities may be way off with only 10 reps, but theoretical probabilities are: .0625, .25, .375, .25, .0625 11.) A. Assume the probabilities in the problem hold true for this situation. Let 1-25 correspond to a passenger who fails to appear and 26-100 correspond to a passenger who does appear. Choosing 9 numbers represents 1 repetition. Probability=0.3003

6.2 Probability

probability probability (theoretical) of any random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions empirical probability--based on observations/experience Ex: simulation

probability A) Event is impossible B) Event is certain—happens every time C) Event is very unlikely, occurs once in a while D) Event will occur more often than not

probability Probability Model—2 Parts: 1. sample space—set of all possible outcomes 2. probabilities assigned to each event

probability Examples: Toss 1 coin: Toss 2 coins: H T H T H T

probability Examples: Roll 2 dice: 1 2 3 4 5 6 Examples: Toss 3 coins: H T H T multiplication principle—how many are in the sample space

Probability rules 1. Probability has to be between 0 and 1 2. Sum of probability of all possible outcomes must equal 1 3. If A and B are disjoint (mutually exclusive)—cannot happen at the same time A B

Probability rules 4. The probability that A does not occur is equal to Complement of A = A does not occur

Probability notation union— intersect— empty set—

Benford’s law example Legit tax records follow this distribution: 1 2 1st digit 1 2 3 4 5 6 7 8 9 Prob .301 .176 .125 .097 .079 .067 .058 .051 .046

HW: pg. 416 #30, 33, 36 pg. 423 #37, 40