1. 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, : republican

2. 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, ) A. Assume the probabilities in the problem hold true for this situation. Let 1-25 correspond to a passenger who fails to appear and correspond to a passenger who does appear. Choosing 9 numbers represents 1 repetition. Probability=0.3003

3. 6.2 Probability

4. 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

5. 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

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

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

8. 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

9. 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

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

11. Probability notation
union—
intersect—
empty set—

12. 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

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