1. February 19, 2016

2.  Symbol: - What they have in common  Events A and B are ________________ if: Knowing that one occurs ______________ change the probability that the other occurs.  Rule: P(A and B) =  AND means to _____________!!

3.  Events A and B are _______________ if:  One event _________ change the probability of the next event.  The General Rule:  P(A and B)=  In other words:

4. 1) What is the probability of getting a heads and a tails? 2) What is the probability of being dealt a red card and then another red card from a standard deck of cards without replacement?

5.  Disjoint or mutually exclusive ____________ be independent!!  If A and B are disjoint, then the fact that A occurs tells us that B _____________ occur.

6. A general can plan a campaign to fight one major battle or 3 small battles. He believes he has a probability of.6 of winning the large battle and a probability of.8 of winning each small battle. Victories or defeats in small battles are independent. The general must win either the large battle or all three of the small battles. Which strategy should he choose?

7. A string of Christmas lights contains 20 lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability of 0.02 of failing during a 3-year period. The lights fail independently of each other. What is the probability that the string of lights will remain bright for 3 years?

8. An athlete suspected of having used steroids is given two tests that operate independently of each other. Test A has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroids have been used. What is the probability that Test A and Test B both come back negative for steroid use?

9.  Can use the Multiplication Rule to show independence:  So… If then the two events are independent

10.  For events C and D, P(C) = 0.7 and P(D) = 0.3 and P(C U D) = 0.9. Find Are C and D independent? Why or why not?

11. Back to our Pierced Ear Example Pierced Ears? GenderYesNoTotal Male197190 Female84488 Total10375178  If we know that a randomly selected student has pierced ears, what is the probability that the student is male?  If we know that a randomly selected student is male, what is the probability that the student has pierced ears?

12. The probability that one event happens _______ __________ another event is already known to have happened is called _____________ probability The probability that event B happens given that event A has happened is denoted by ________ CAUTION: Order matters here! The given piece will tell you what the denominator will be

13. Students at the University of New Harmony received 10,000 course grades last semester. The following table breaks down these grades by which school of the university taught the course. The schools are “Liberal Arts (LA)”, “Engineering and Physical Sciences (EPS)” and “Health and Human Services (HHS) ”. Grade Level ABBelow BTotal LA2142189022686300 EPS3684328001600 HHS8826305882100 Total33922952365610,000

14. a. What is the probability that a grade is not an A? b. What is the probability that a grade is a B or better? c. What is the probability that a grade is an A, given that it comes from an HHS course? d. What is the probability that a grade is not a B, given that it comes form an EPS course? e. What is the probability that a grade is an A or below B, given that it comes from an LA course?

15. Now consider the two events E: the grade comes from an EPS course, and L: the grade is lower than a B. f. Find P(E)g. Find P(L) h. Find P(E L)i. Find P(L E)

16.  We can use the Multiplication Rule to do other forms of conditional probability problems…we need to rewrite the formula

17. In an apartment complex, 40% of residents read USA Today. Only 25% read the New York Times. Five percent of residents read both papers. Suppose we select a resident of the apartment complex at random and record which of the two papers the person reads. Question: What is the probability that a randomly selected resident who reads USA Today also reads the New York Times?

18. In a school of 1200 students, 250 are seniors, 150 students take math, and 40 students are seniors and are also taking math. What is the probability that a student is taking math, given that the student is a senior?