Transcript Stat 100
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.