Question

As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in 2012. (Source: Pew Research Center for the People and the Press). Each house-hold, of course, is independent of the others. Using the cooperation rate from 2012

b)what is the probability of failing to contact a house-hold or of contacting the household but not getting them to agree to the interview?

--> I did this one using P(A,B and C) = P(A) + P(B) x P(C)

P(A) = next household will fail to be contacted
P(B) = next household will be contacted
P(C) = household will refuse the interview

THE QUESTION I NEED HELP WITH:

c) show another way to calculate the probability in b)

--> I'm having issues trying to figure out another way to solve this without using the same method as above....

Thanks!

Answer 1

The other way would be a shorter way.

For this, we need to find out the probability that the household was contacted and have agreed to cooperate with the survey.

So, the probability (in 2012) would be = 0.62 * 0.14

= 0.0868.

And the probability of either not being able to contact the household or the probability that the household, if contacted does not agree to cooperate with the survey =

1 - probability that the household was contacted and have agreed to cooperate with the survey

= 1 - 0.0868

= 0.9132.

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