Question

Working on summer vacation.Refer to the Harris Interactive(July 2013) poll of whether U.S. adults workduring summer vacation, Exercise 3.13 (p. 169). Recall thatthe poll found that 61% of the respondents work duringtheir summer vacation, 22% do not work at all while onvacation, and 17% were unemployed. Also, 38% of thosewho work while on vacation do so by monitoring theirbusiness emails.

a.Given that a randomly selected poll respondent will work while on summer vacation, what is the probability that the respondent will monitor business emails?

b.What is the probability that a randomly selected poll respondent will work while on summer vacation and will monitor business emails?

c.What is the probability that a randomly selected poll respondent will not work while on summer vacation and will monitor business emails?

Short answer

1. 0.38
2. 23.18%
3. 0

Step-by-step solution

 Step 1: Finding the probability that the respondent will monitor business emails while on summer vacation

P(A) = Respondents will monitor business emails = 38% = 0.38

Therefore, the probability that a respondent will monitor business emails while on summer vacation is 0.38.

Calculating the probability that the respondent will work during vacation and monitor business emails

P(A) = Respondents will monitor business emails while on vacation = 0.38

P(B) = Respondent will work on summer vacation = 0.61

$\begin{array}{c}\text{P}\left(\text{AÇB}\right)\text{=P}\left(\text{A}\right)\text{×P}\left(\text{B}\right)\\ \text{=0.38×0.61}\\ \text{=0.2318}\\ \text{=23.18\%}\end{array}$

Hence, the probability that the respondent works during the vacation and monitors email is 23.18%.

Finding the probability that a respondent will not work on vacation and monitor emails 

P (A) = Respondent does not work on vacation = 22% = 0.22

P (B) = Respondents monitor emails = 38% = 0.38

The probability of both A and B occurring together is 0because the respondent who does not work at all on vacation will not monitor business emails.