Stat 100 Feb. 18

Stat 100 Read Chapter 15 Try 1-5, 7, 14, 17, 18, 21, 25

Two Possible Interpretations of Probability Relative Frequency Personal Probability

Relative Frequency Interpretation Probability is fraction of times an event will occur over many repeated trials or observations Example: Probability of winning lottery.

Personal Probability A subjective or personal number that reflects the chance of something Example: What do you think is the probability that you’ll graduate within four years of starting college?

Assignment of Probabilities Probabilities might be assigned using: physical model observation of long run personal subjectivity

Probability Values Probabilities are numbers between 0 and 1. 0= event never occurs 1=event always occurs

Opposite Events Suppose the chance you you buy a new car this year is .10. What’s the chance you do not buy a new car this year? Answer=1-.10=.90 Rule: Prob of event = 1  Prob of opposite event

Independence and Dependence Two events are independent if the chance one occurs is not affected by whether or not the other occurs Two events are dependent if the chance one occurs is affected by whether or not the other occurs

Example Are the results of two coin flips independent or dependent? Answer = Independent One card is drawn from a 52-card deck. Then, a second card is drawn. Are the results independent or dependent? Answer = Dependent

Example Suppose 20 of 200 women day they like to gamble. And, 45 of 180 men say they like to gamble Are liking to gamble and gender independent or dependent characteristics?

Multiplication Rule Multiply probabilities to find the chance that two or more events occur together or in a sequence.

Examples Chance you correctly guess at two true-false questions is (1/2)(1/2)=1/4 What is the chance you correctly guess at 5 True-False Questions? Answer = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32

Example Group includes 3 men and 2 women Two people are picked randomly. What is the probability both are women? Answer = (2/5)(1/4) = (2/20) = 1/10 What is the probability that one woman and one man are picked?

A Spectacular Coincidence ? Several states draw four digit lottery numbers Several years ago Mass. and N.H both drew the same number on the same night Associated Press wrote that this was a spectacular 1 in 100 million coincidence

Was the AP Right ? Only if number picked was specified before draws are made Chance both pick the same pre-specified number is (1/10,000) (1/10,000) This is 1 in 100 million

The correct analysis First state could picked any number Prob that second state matches is 1/10,000 Multiplication is 1x(1/10,000)=1/10,000 Even this, may not be right.

The Right Problem At the time, 15 states were drawing 4-digit numbers Right problem could be: What’s chance that 2 of 15 states match? This has turns out to be about 1 in 100.