1. Stat 100
Feb. 18

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

3. Two Possible Interpretations of Probability
Relative Frequency
Personal Probability

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

5. 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?

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

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

8. Opposite Events
Suppose the chance you you buy a new car this year is 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

9. 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

10. 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

11. 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?

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

13. 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

14. 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?

15. 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

16. 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

17. 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.

18. 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.