Question

​Opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 60​% of​ households, the percentage of those contacted who agree to cooperate with the survey is only 37​%. Each household is independent of the others.
​a) What is the probability that the next house will be contacted and refuse to​ cooperate? ​
b) What is the probability of failing to contact a​ house, or making contact and not getting them to agree to the​ interview? ​
c) Show the reasonable ways to calculate the probability in part b.

Answer 1

Answer:

a) The probability that the next house will be contacted and refuse to​ cooperate is 0.378

b) The probability of failing to contact a​ house, or making contact and not getting them to agree to the​ interview is 0.778

c) The probability of failing to contact a​ house, or making contact and not getting them to agree to the​ interview is the sum of both probabilities:

1. the probability of failing to contact a​ house. it is equal to 0.4

2. the probability of making contact and not getting them to agree to the​ interview. It is equal to 0.378

P =  0.4 + 0.378 = 0.778

Step-by-step explanation:

From the question we know that interviewers reach 60% of the households and from those who are contacted, 37% is agree to cooperate with the survey. That's mean that the 63% of the reached household refuse to cooperate.

So the probability that the next house will be contacted and refuse to cooperate can be calculate as:

P=                   0.6                        *                     0.63                  = 0.378

   Reach the households          and   refuse to cooperate

For part b, we need to identify and sum 2 independent probabilities:

1.  the probability of failing to contact a​ house

2. the probability of making contact and not getting them to agree to the​ interview.

From part a we know that 0.378 is the probability of making contact and not getting them to agree to the interview.

Additionally, the probability of failing to contact a house is 0.4 because this probability is the complement of the probability of reach a household. This is calculate as:

1-0.6=0.4

Then the probability of failing to contact a​ house, or making contact and not getting them to agree to the​ interview is the sum of both probabilities:

P =  0.4 + 0.378 = 0.778