AC Geo/Adv Alg U4 Worksheet 6 Name____________________________ FINDING PROBABILITIES USING TWO-WAY TABLES: Two-way tables are another method of organizing data that represents a sample space. Using the information presented in the table, we can find probabilities that will lead us toward being able to determine if there is a relationship between events (i.e. are events independent?). EXAMPLE: Gender vs. Income – Has the gender gap closed in the world today? Are men and women able to earn the same amount of money? The table below organizes income levels (per year) and gender. Male Female Under $10,000 15 31 Between $10,000 and $40,000 64 73 Between $40,000 and $100,000 37 14 Over $100,000 61 58 First we should define some events to make our notation easier: Let M= Let A= Let F= Let B= Let C= Let D= If we were to randomly pick a person from this sample space, find the probability of each of the events we just defined. P(M)= P(A)= P(C)= P(F)= P(B)= P(D)= ANSWER THE FOLLOWING USING APPROPRIATE PROBABILITY NOTATION: What is the probability you randomly choose a female that makes over $100,000? What is the probability you randomly choose a female or someone that makes over $100,000? What is the probability you choose a person that makes over $100,000 , given they are female? What is the probability you choose a person that makes over $100,000 , given they are male? Do you think being female and making over $100,000 are independent events? Explain. We now have two ways we can test to see if events are independent 1) P(A)=P(A│B) OR 2) P(A∩B)=P(A) •P(B) Based on these calculations, do you think there is some evidence of a relationship between gender and income? Further statistical analysis is needed before conclusions can be drawn. You will learn about this in other courses. Assignment: U4 WS 6 Exercises 1-4, use the data in the table below, which shows the employment status of individuals in a particular town by age group. Age Group 0-17 18-25 26-34 35-49 50+ Full-time 24 185 348 581 443 Part-time 164 203 67 179 162 Unemployed 371 148 27 104 173 1 If a person in this town is selected at random, find the probability it is a 35 and 49 year old that works parttime. 2. If a person in the town is randomly selected, what is the probability that the individual is unemployed, given that he or she is over 50 years old? 3. A person from the town is randomly selected; what is the probability that the individual is employed full-time, given that he or she is between 18 and 49 years of age? 4. A person from the town is randomly selected; what is the probability that the individual is employed parttime, given that he or she is at least 35 years old? Exercises 5-8, use the data in the following table, which shows the results of a survey of 2000 gamers about their favorite home video game systems, organized by age group. If a survey participant is selected at random, determine the probability of each of the following. Sony PlayStation 2 0-12 63 13-18 105 19-24 248 25+ 191 Totals 607 Microsoft Xbox 84 139 217 166 606 Nintendo GameCube 55 92 83 88 318 Sega Dreamcast 51 113 169 136 469 Totals 253 449 717 571 2000 5. The participant prefers the Sony PlayStation 2 system. 6. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and 18. 7. The participant prefers Nintendo GameCube, given that the person is between the ages of 13 and 24. 8. The participant is under 12 years of age, given that the person prefers the Sega Dreamcast machine. A survey at a school asked students if they were ill with a cold or the flu during the last month. The results were as follows. None of the students had both a cold and the flu. For 9-12, use these results estimate the probability that.. Females Males Cold 32 25 Flu 18 19 Healthy 47 38 9. a randomly selected student had a cold in the last month 10. a randomly selected student had the flu, given that they are female. 11. a randomly selected student is a male with the flu. 12. a randomly selected student had either a cold or the flu last month. Exercises 13-17, use the table below to complete the problems. The question, "Do you play football?" was asked of 110 students. Results are shown in the table. 13. What is the probability of randomly selecting an individual that is a boy and who plays football? 14. What is the probability of a randomly selecting an individual that is a boy? 15. What is the probability of a randomly selecting an individual that plays football? 16. What is the probability of a randomly selecting a boy, given they play football? 17. What is the probability that a randomly selecting a football player, given that they are a boy? 18. You roll two dice. The first die shows a TWO and the other die rolls under the table and you cannot see it. Now, what is the probability that both die show TWO? 19. In a box are a carton of dairy milk and Boonville chocolates. Two items are chosen at random from the box, without replacement. The probability of selecting dairy milk and a Boonville chocolate is 0.47. The probability of selecting dairy milk on the first draw is 0.71. What is probability selecting a Boonville chocolate on the second draw, given that the first chocolate drawn was dairy milk?
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