April 15, Chapter 5 Section 3 day s.notebook. Honors Statistics. Aug 23-8:26 PM. Apr 9-2:22 PM

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1 Honors Statistics Aug 23-8:26 PM Apr 9-2:22 PM 1

2 3. Review Homework C5#5 Aug 23-8:31 PM Dec 1-5:05 PM 2

3 A Skip 52, 55 How do you want it - the crystal mumbo-jumbo or statistical probability? Apr 25-10:55 AM Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has the following information about its customers: 20% are currently undergraduate students in business; 15% are undergraduate students in other fields of study; 60% are college graduates who are currently employed; and 5% are college graduates who are not employed. Choose a customer at random. P(Undergrad and Business) = 0.20 P(Undergrad and other) = 0.15 P(Grad and Employed) = 0.60 P(Grad and not employed) = 0.05 Notice that all the Probabilities add up to 1.00 (a) What s the probability that the customer is currently an undergraduate? Which rule of probability did you use to find the answer? P(Undergrad) = P(Undergrad and Business) + P(Undergrad and other) = 0.35 or 35% I can add these because the events (Undergrad Bus) and (Undergrad other) are mutually exclusive. (b) What s the probability that the customer is not an undergraduate business student? Which rule of probability did you use to find the answer? NOT Law of complements P(Undergrad Business c ) = = 0.80 Nov 15-6:28 PM 3

4 Sampling senators The two-way table below describes the members of the U.S Senate in a recent year If we select a U.S. senator at random, what s the probability that the senator is (a) a Democrat? (b) a female? 60 P(Democrat) = = P(Female) = = (c) a female and a Democrat? 13 P(Female and Democrat) = = (d) a female or a Democrat? Two ways to do this problem Way 1 - Using the General Addition formula Way 2 - Using the table counts P(Female or Democrat) = P(Female) + P(Democrat) - P(Female and Democrat) P(Female or Democrat) = = = P(Female or Democrat) = = = Nov 15-6:09 PM Playing cards Shuffle a standard deck of playing cards and deal one card. Define events J: getting a jack, and R: getting a red card. (a) Construct a two-way table that describes the sample space in terms of events J and R. Jack Jack C Red Red C (b) Find P(J) and P(R). 4 P(J) = = P(R) = = (c) Describe the event J and R in words. Then find P(J and R). 2 The card is a red jack or the card is red and a jack. P(J and R) = = (d) Explain why P(J or R) P(J) + P(R). Then use the general addition rule to compute P(J or R). The events card is red and card is a jack are not mutually exclusive... thus one will count two cards twice unless using the general probability addition formula P(J U R) = = = P(J U R) = = = OR Nov 15-6:00 PM 4

5 Who eats breakfast? Refer to Exercise 49. (a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male. B M (b) Find P(B M). Interpret this value in context P(B U M) = = = P(B U M) = = = OR the probabililty that person is a male or eats breakfast regularly (or both) = 72.3% (c) Find P(B C M C ). Interpret this value in context. P(B C M C 165 ) = = the probabililty that a person is not a male and does not eat breakfast is 27.7% Nov 15-6:33 PM Sampling senators Refer to Exercise (a) Construct a Venn diagram that models the chance process using events R: is a Republican, and F: is female R F (b) Find P(R F). Interpret this value in context P(R U F) = = = P(R U F) = = = OR the probabililty that a senator is a Republican or a Female (or both) = 53% (c) Find P(R C F C ). Interpret this value in context. P(R C F C 47 ) = = the probabililty that a senator is a not Republican and not Female = 47% Nov 15-6:33 PM 5

6 Facebook versus YouTube A recent survey suggests that 85% of college students have posted a profile on Facebook, 73% use YouTube regularly, and 66% do both. Suppose we select a college student at random. (a) Make a two-way table for this chance process. FACE N F UTube N U (b) Construct a Venn diagram to represent this setting. U T 0.07 Face (c) Consider the event that the randomly selected college student has posted a profile on Facebook or uses YouTube regularly. Write this event in symbolic form based on your Venn diagram in part (b). P(Face or UTube) = P(F U T) = (d) Find the probability of the event described in part (c). Explain your method. P(F U T) = P(F) + P(T) - P(F T) = = 0.92 OR USing VENN DIAGRAM P(F U T) = = 0.92 Nov 15-6:33 PM Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (Macs). The rest mainly used PCs. At the time of the census, 67% of the school s students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their main computers. Suppose we select a student at random from among those who were part of the census. (a) Make a two-way table for this chance process. MAC PC Und 0.30 Grad (b) Construct a Venn diagram to represent this setting. Und 0.37 MAC (c) Consider the event that the randomly selected student is a graduate student and uses a Mac. Write this event in symbolic form based on your Venn diagram in part (b). P(Graduate and MAC) = P(U c and MAC) (d) Find the probability of the event described in part (c). Explain your method. P(Graduate and MAC) = P(U c and MAC) = 0.10 ALTERNATIVE VENN DIAGRAM Grad 0.23 MAC c and d) P(G and MAC) = P(G M) = 0.10 Nov 15-6:33 PM 6

7 Nov 9-5:30 PM Nov 9-5:34 PM 7

8 Please place the following in your pocket folder: Aug 20-8:59 PM Nov 15-10:41 PM 8

9 Nov 15-10:41 PM Nov 15-10:41 PM 9

10 Conditional Probability = P(both events occur) P(given event occurs) Nov 15-10:42 PM May 3-6:11 PM 10

11 May 3-6:12 PM Apr 9-1:59 PM 11

12 (given landline, also cell phone) Nov 15-11:09 PM Nov 28-9:14 PM 12

13 (This table is based closely on grade distributions at an actual university, simplified a bit for clarity.) College grades tend to be lower in engineering and the physical sciences (EPS) than in liberal arts and social sciences (which includes Health and Human Services). Choose a University of New Harmony course grade at random. Consider the two events E: the grade comes from an EPS course, and L: the grade is lower than a B. 1. Find P(L). Interpret this probability in context. 2. Find P(E L) and P(L E). 3. Which of these conditional probabilities tells you whether this college s EPS students tend to earn lower grades than students in liberal arts and social sciences? Explain. The P(L E) gives the probability that a student gets grades lower than B's if they are Engineering students. Because the P(L E) = 0.50 which is higher than just P(L) = this tells us that compared to the rest of the college, engineering students tend to get lower grades more often than nonengineering students. (Well duh... their classes do tend to be harder with more challenging material). Nov 15-11:02 PM Worksheets?? How do you want it - the crystal mumbo-jumbo or statistical probability? Apr 25-10:55 AM 13

14 T P(H T) = 0 Dec 14-8:40 AM Dec 4-8:44 AM 14

15 Dec 14-8:40 AM 15