Stats #6

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Apr 3, 2024

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STAT 1430 Recitation 6 Part 1: Suppose you choose a student at random and you note gender and whether they are wearing a backpack. Write the notation for each of the following. For example P(A), P(A|B), P(A and B). Note, some may have the same answers, but different wording, as you Gind in the media. 1. Probability that a female student is wearing a backpack. P(F) 2. Probability that a student who is wearing a backpack is a female. P(B/F) 3. Probability that a student is wearing a backpack and is female. P(B and F) 4. Probability that a student is male IF they are wearing a backpack. P(M/B) Suppose 40% of your customers have debit cards, and of those customers, 60% use credit cards. You also know that of your customers who don’t have debit cards, 80% use credit cards. Let D=debit card, ND = no debit card, C=credit card users and NC=non-credit card users. 5. Fill in the table using only probability notation, for example P(D) or P(ND and C) or P(D|C). DO NOT CALCULATE ANYTHING OR SHOW ANY FORMULAS. 6. Now using the MULTIPLICATION RULE (see lecture notes), Sill in the appropriate numbers in all parts of the table below. Show all formulas, notation, and calculations for the 4 cells in the table. Then just sum to get the marginal totals. (Work - next page) Credit Card No Credit Card Total Debit card P(C and D) P(NC and D) P(D) = .4 No debit card P(C and ND) P(NC and ND) P(ND) = .6 Total P(C) P(NC) 1 Credit Card No Credit Card Total Debit card 0.4 x 0.6 = 0.24 0.4 x 0.4 = 0.16 0.4 No debit card 0.6 x 0.8 = 0.48 0.6 x 0.2 = 0.12 0.6

STAT 1430 Recitation 6 S uppose you examine whether your customers are aged under 18, or 18 and over, and whether they made a purchase at your store. Your results are in the following table: Let U = Under 18, NU = 18 or over, P=purchase, and NP=no purchase. Answer the following questions using probability notation, such as P(P|U) or P(NU and NP). 7. Using notation, what probability does .17 represent? What type of probability is this, conditional, marginal, ‘and’? - P(P and NU), And 8. Using notation, what probability does .15 represent? What type of probability is this, conditional, marginal, ‘and’? - P(P and U) , And 9. Using notation, what probability does .40 represent? What type of probability is this, conditional, marginal, ‘and’? - P(U), Marginal 10. Using notation, what probability does .25 represent? What type of probability is this, conditional, marginal, ‘and’? - P(NP and U), And 11. If we took .15/.40, what probability does this represent? Use notation. What type of probability is this, conditional, marginal, ‘and’? - P(P and U)/ P(U) = P(P/U) conditional 12. If we took .15/.32, what probability does this represent? Use notation. What type of probability is this, conditional, marginal, ‘and’? - P(U/P), Conditional Voter Statistics Statistics Brain Research Institute reports the following information regarding voters: • 70% of all U.S. Citizens are registered to vote. • 69% of U.S. males are registered to vote. • 73% of U.S. females are registered to vote. Total 0.72 0.28 1 Under 18 18 or over Total Purchase .15 .17 .32 No Purchase .25 .43 .68 Total .40 .60 1

STAT 1430 Recitation 6 Given the above information: 13. Write down probability notation for “70% of all U.S. citizens are registered to vote.” - P(M and F) 14. Write down probability notation for “69% of U.S. male citizens are registered to vote.” - P(M/R) 15. Write down probability notation for “73% of U.S. female citizens are registered to vote.” - P(F/R) 16. Independence a. Make 2 pie charts (using StatCrunch) to illustrate the information about the % of males and females being registered to vote, compared to the overall percentage of registered voters. SHOW THE PIE CHARTS HERE: b.Using the above information, is gender independent of being registered to vote? Explain your answer. No, the conditionals aren’t the same 17.Find another website where voter registration statistics are presented by another variable that is NOT gender. Write down your source, and the results. https://www.census.gov/newsroom/press-releases/ 2021/2020-presidential-election- voting-and-registration-tables-now-available.html 18.True or False: P(A|B) = 1- P(not A | B). a.True b.False 19.Give a real world example of why your answer to the previous problem is true or false. Example: A = you like onions and B = you own a cat. P(A/B) -> given that they own a cat what is the probability they like onions 1- P(Not a/b) -> given that they own a cat what is the probability that they don’t own onions minus one. Both are the same since they are both getting at the same point. Make 3 calls. Each call has a 10% chance of making a sale.

STAT 1430 Recitation 6 20. Make 3 calls. Each call has a 10% chance of making a sale. a. Write down the entire sample space S for the 3 calls. Hint: There are 8 outcomes. 1. S - S - S 2. S - S - N 3. S - N - S 4. S - N - N 5.N - S - S 6.N- S - N 7.N - N - S 8. N- N- N b. Write down the probability for each outcome and circle the outcomes that have the same probability. 1 - 0.001 2 - 0.009 3 - 0.009 4 - 0.081 5 - 0.009 6 - 0.081 7 - 0.081 9 - 0.792 c. What is common about the items that were circled? They both have the same amount of sales vs. no sales Part 2: 1. The following table shows data from a sample of 100 drivers who own cars. Number of speeding ;ckets in the last 6 months, and whether or not they drive a fast car were recorded. (Fast car is defined as a car capable of going at high speeds.) Based on the data above, are owning a fast car and geEng more than 1 speeding ;cket independent? A. YES B. NO >1 speeding ;cket Got 0 or 1 speeding ;ckets Has a fast car 12 3 Doesn’t have a fast car 19 66

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