(c) Given that a respondent from age 12~50 is selected, what is the probability that the respondent believe email messages should be answered quickly?

Question Completion:

Do people of different age groups differ in their response to email messages? A survey reported that 71.3% of users over 70 years of age believe that email messages should be answered quickly, as compared to 52.5% of users 12 to 50 years old. Suppose that the survey was based on 1, 000 users over 70 years of age and 1, 000 users 13 to 50 years old. The table summarizes the results.

          Answers Emails Quickly

Age         12 - 50     Over 70         Total

Yes          525             713             1,238

No            475            287               762

Total     1,000          1,000           2,000

Given that a respondent from age 12 to 50 is selected, what is the probability that the respondent believes that email messages should be answered quickly?

The probability that the respondent, aged 12 to 50, believes that email messages should be answered quickly is:

= 52.5%

Step-by-step explanation:

Data and Calculations:

          Answers Emails Quickly

Age         12 - 50     Over 70         Total

Yes          525             713             1,238

No            475            287               762

Total     1,000          1,000           2,000

Aged 12 - 50:

Probability of answering emails quickly = Yes/Total = 525/1,000 * 100 = 52.5%

Probability of not answering emails quickly = No/Total = 475/1,000 * 100 = 47.5%

Aged over 70:

Probability of answering emails quickly = Yes/Total = 713/1,000 * 100 = 71.3%

Probability of not answering emails quickly = No/Total = 287/1,000 * 100 = 28.7%

b) The probability of an event happening (answering an email quickly by those aged 12 to 50) is the chance that this age group will respond to their emails quickly.  It is computed as the number of times that this age group responds to emails quickly divided by their total response to emails.  The quotient is then expressed as a percentage.