Warm Up Wed/Thurs. Do #17 p. 341 You will want this on a piece of paper to KEEP for reference.

Probability Models 6.3 A) Use your calculator to store SHAQ B) He hit 47% of his shots for me. How about you? C) I had 5 Hits in a row and 5 Misses in a row.

6. 5 There are 21 zeroes in the first 200 digits of the RDT 6.5 There are 21 zeroes in the first 200 digits of the RDT. This seems very logical because its ratio has a proportion of .105 which is very close to 0.1.

6.12 S = {0 – 24} S = {0,1,2,3,...10,998, 10,999, 11,000} S = {0,1,2,3,4,5,6,7,8,9,10,11,12} S = {0, .01, .02, .03,…………} S = {...negative grams, 0, positive grams…}

I love probability  6.15 a) 10 X 10 X 10 X 10 10000 county license tags b) 10 X 9 X 8 X 7 5040 county license tags c) 104 + 103 + 102 + 101 11, 110 county license tags

6.18 Red card = 26 ways Heart = 13 ways Queen and a heart = 1 way Queen or a heart = 13 ways for heart and 4 queens – 1 queen ♥ = 16 ways Queen that is not a heart = 3 ways

Probability is cool. 6.19 The probability of type AB blood would be 1-.49-.27-.20=.04 P(O) + P (B) = .49 + .20 = .69 is the probability that a randomly chosen black American can donate to Maria. 6.21 The probability that the death was due to either cardio or cancer is .45+.22 = .67. The probability that the death was due to some other cause is 1-.45-.22 = .33.

6.23 a) The sum of the probabilities is 1. Probability Rule #2, all possible outcomes together must sum to 1. b) The probability that a randomly chosen first year student was not in the top 20% is 1-.41=.59 c) The probability that a randomly chosen first year student was in the top 40% is .41+ .23 =.64

Benford’s Law 1st Dig 1 2 3 4 5 6 7 8 9 Prob. .301 .176 .125 .097 .079 .067 .058 .051 .046

6.26 D is defined as the 1st digit is less than 4 so P(D) = .301 + .176 + .125 = .602 P( B U D) = (.067+.058+.051+.046) + (.602) = .824 P(D)c = 1-.602 = .398 P(C n D) = P ( odd and <4) = P (1) + P (3) = .301 + .125 = .426 P(B n C) = P ( ≥6 and odd) = P (7) + P (9) = .058 + .046 = .104

6.30 P(A)={the person chosen completed 4 yrs college} P(B)={the person chosen is 55 years old or older} a) P(A)= #people completing 4 yrs resident >25 yrs of age = 44845/175230 = .2559 or .256 b) P(B)= #people 55 yrs older = 56008/175230 = .3196 or .32 c) P(A and B)= #people 55 yrs older and 4 yrs of college = 10596/175230 = .0605 = .061

Data on people controlling their weight that have diabetes or do not have diabetes. TWO-WAY TABLES Total columns/rows are marginal distributions. You can also give them in percents. The first thing you should do for a two way table is to calculate these!!!!

Find the percent of controlled and uncontrolled people with diabetes? 20%, 82% THIS IS CALLED CONDITIONAL DISTRIBUTION!! How many people are being described? 5167 What percent of the people without diabetes have their weight under control? 42%

BACK TO PROBABILITY!! An event is any outcome or a set of outcomes of a random phenomenon. An event is a subset of the sample space. A probability model is a mathematical description of a random phenomenon. Consists of two parts: a sample space, S and a way of assigning probabilities to events.

Where do probabilities come from? Probabilities may be given, often in the form of a table. For example, if an experiment has three possible outcomes: Apple, Banana, and Cherry, one might be given the following table at the right : Probabilities my be historical, if it has rained during 1/3 of the days in June during the past, one may say that the probability of rain for a day in June is 1/3. Probabilities may be theoretical, if a die is fair, since there are six possible outcomes; the probability of getting a 3 is 1/6. Apple .5 Banana .3 Cherry .2

Discrete vs. Continuous If the experiment is to throw a standard die and record the outcome, the sample space is: S = {1, 2, 3, 4, 5, 6}, the set of possible outcomes. Discrete sample space Finite number of outcomes On the other hand, if the experiment is to randomly pick a number between 0 and 1, then the sample space is to be S = [all #’s between 0 and 1], Continuous sample space Infinite number of outcomes

Replacement v. Non-replacement If you are selecting objects from a finite group of objects, whether you replace the object is very important. If you do not replace, then the probability for each selection will change. If we sample with replacement, each item is replaced in the population before the next draw; thus, a single object may occur several times in the sample. If we sample without replacement, objects are not replaced in the population.

Probability Rules #1 Probability is a number from 0 to 1. #2 All possible outcomes together must have the probability of 1. ( there sum = 1) #3 If two events have no outcomes in common, P(A or B)= P(A) + P(B). #4 Events A and B are independent if P(A and B)= P(A)P(B).

Example: 3 marbles are drawn from a jar of 4 yellow, 5 blue, and 2 red. What is the probability of getting 3 blue. With replacement Without replacement REMEMBER TO MULTIPLY WITH INDEPENDENT EVENTS!!!!

Homework Finish Reading 6.2 Do #’s 35 - 45 Read and Take notes on Chapter 4.3 p241-255 do #’s 50 - 53, 60,83