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Gain Confidence with Probability: The Two-Way Table 1-19. AN ASSOCIATION? The Collectable Card Club wants to take a trip to their State’s Card-a-Con. Tonya is trying to gather information to order club t-shirts in either male or female cuts, and arrange carpools, so she takes a census of the club’s members. 31 males, 9 females, 13 members with cars, 27 without cars. She also notices that only one-third of the girls have cars. 3-31. a. Use her census information to make an appropriate chart or graph. b. Tonya is convinced there is a relationship between the variables ‘gender’ and ‘having a car.’ Do you agree with Tonya? Justify your reasoning. In Canada, 92% of the households have televisions. 72% of households have televisions and Internet access. 5% have neither. a. Create a relative frequency table of this situation. b. What is the probability of selecting a Canadian house at random that has Internet access but no television? c. What is the conditional probability of selecting a house that has Internet given that it has a television? d. Of the houses that do not have television, what is the conditional probability of selecting one that has Internet access? e. Is there an association between television ownership and Internet access in Canadian homes. Provide evidence. © 2013 CPM Educational Program. All rights reserved 1 Gain Confidence with Probability: The Two-Way Table 3-27. APPLES AND BANANAS Let event “A” represent a randomly selected high school student ate an apple at lunch and event “B” represent the student ate a banana at lunch. The event did NOT eat an apple is then A and did NOT eat a banana is B . B B A 0.20 0.10 0.30 A 0.45 0.25 0.70 0.65 0.35 The right notation can save a lot of explaining. For example, answer each of the next two questions in a complete sentence: a. P(B) = ______ b. P( A ) = ______ The symbol stands for the “union” and represent the “or” condition, while the symbol stands for “intersection” and represents the “and” condition. Often the symbol “ | ” is used to represent “given that”. P(G | H) represents the probability of G given that H has occurred. Convert the following language to probability notation and find the probabilities associated with randomly selecting a high school student who c. ate a banana and an apple at lunch. d. ate a banana or did not eat an apple at lunch. e. did not eat a banana and ate an apple at lunch. f. ate a banana given that they ate an apple at lunch. B Here is the Apples and Bananas table with the relative frequencies removed. Some of the relative frequencies have been replaced with their associated probability notations. g. B A P(A) P( A ∩ B ) A P(B) Fill in the other missing relative frequencies with the correct probability notation. © 2013 CPM Educational Program. All rights reserved 2 Gain Confidence with Probability: The Two-Way Table 3-30. Here is the Apples and Bananas table again with all of the relative frequencies removed and replaced with their associated probability notations. B B A P(A B) P(A B ) P(A) A P( A B) P( A ∩ B ) P( A ) P(B) P( B ) Using only probability notation, (no numbers) create expressions which represent the events shown in parts (a) through (d). Do not use the A or B symbols. 3-39. a. P(B | A) = b. P(A | B) = c. P(A B) = d. Now consider a case where you were given a conditional probability such as P(A | B) along with P(B). Show symbolically how you could get the joint probability P(A B). Of the students who choose to live on the East Coast College campus, 10% are seniors. The most desirable dorm is the newly constructed Ocean View dorm, and 60% of the seniors who live on campus live there, while 20% of the rest of the oncampus students live there. a. Represent these probabilities in a graphical display (tree, and/or relative frequency table). b. What is the probability that a randomly selected resident of the Ocean View dorm is a senior? © 2013 CPM Educational Program. All rights reserved 3 Gain Confidence with Probability: The Two-Way Table 5-21. Governments and security companies are coming to rely more heavily on facial recognition software to locate persons of interest. Consider a hypothetical situation. Suppose that facial recognition software can accurately identify a person 99.9% of the time, and suppose the suspect is among 200,000 facial images available to a government agency. When the software makes a positive identification, what it the probability that it is not the suspect? 9-26. a. Make a two-way table for this situation. b. If a person has been identified as the suspect, what is the probability that he or she is not actually the suspect? People of Madelinton are security-conscious and have sophisticated car alarms installed on their cars. Over the course of a year these alarms correctly distinguish between a break-in attempt and other harmless events at a 99% rate. Of the 820,600 cars in Madelinton about 100 are broken into each year. If a citizen of Madelinton hears a car alarm, what is the probability the car is being broken into https://ebooks.cpm.org/apstat/ap_stats_problem_gen_v1.0/index.html © 2013 CPM Educational Program. All rights reserved 4