A 2010€“2011 poll conducted by Gallup, (www.gallup.com/poll/148994/Emotional-Health Higher- Among-Older-Americans.aspx) examined the emotional health of a large number of Americans. Among other things, Gallup reported on whether people had an Emotional Health Index score of 90 or higher, which would classify a person as being emotionally well-off. The report was based on a survey of 65,528 people in the age group 35€“44 years and 91,802 people in the age group 65€“74 years. The following table gives the results of the survey, converting percentages to frequencies.

a. If one person is selected at random from this sample of 157,330 Americans, find the probability that this person
i. Is emotionally well-off
ii. Is in the 35€“44 age group
iii. Is emotionally well-off given that this person is in the 35€“44 age group
iv. Is emotionally not well-off given that this person is in the 65€“74 age group
b. Are the events emotionally well-off and emotionally not well-off mutually exclusive? What about the events emotionally well-off and 35€“44 age groups? Why or why not?
c. Are the events emotionally well-off and 35€“44 age groups independent? Why or why not?

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35-44 Age group 65-74 Age group Emotionally Well-Off 16,016 32,583 Emotionally Not Well-Off 49,512 59,219