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.

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

okay wait before i answer, is this for your points on a graph?