The S&P 500 is a stock market index that measures the stock performance of 500 large companies listed on stock exchanges in the U. S. The following table lists the relative frequencies for S&P performance (i.e., whether the index was higher or lower) for the first week of a year and for the year, using 57 years of data. S&P 500 Relative Performance Higher for the Lower for The Total Year Year Higher in 1st Week 0.544 0.088 0.632 Lower in 1st 0.193 0.175 Week 0.368 Total 0.737 0.263 1.000 If a year is selected at random, what is the probability that the S&P 500 finished higher for the year given that it also finished higher in the first week? .861 .737 .544 825 Question 14 (5 points) 20% of American households reported earning $90,000 or more in the 2010 Census. A Gallup Poll found that 21% of Americans reported that they smoked, but that this number decreases with income; only 13% of Americans smoked and lived in households earning $90,000 or more. What is the probability that an American either smoked or lived in a household earning $90,000 or more? 41% 28% 33% 34% Previous Page Next Page Page 14 of 20 Question 15 (5 points) Saved Assume a balanced coin is flipped five times. What is the probability that the last two coin tosses land on heads if the first three tosses landed on heads? .875 .50 .25 0.031 Previous Page Next Page Page 15 of 20 Question 16 (5 points) The following table reports relative frequencies for various modes of public transportation and the usual ways that people pay for the service: Cash Taxi Bus Rail Uber TOTAL 0.080 0.083 0.040 0.050 0.253 Credit 0.067 0.033 0.157 0.223 0.480 City Pass 0.050 0.107 0.110 0.000 0.267 TOTAL 0.197 0.223 0.307 0.273 1.000 Based on these data, it appears that taking Uber and using a City Pass are independent events. Omutually exclusive and independent events. neither mutually exclusive nor independent events. Omutually exclusive events. Previous Page Next Page Page 16 of 20 Question 17 (5 points) Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals .06 0 .80 .70 Previous Page Next Page Page 17 of 20