Chapter 14, Problem 29E

a)

To determine

To find probability that the next household on the list will be contacted but will refuse to cooperate.

Answer to Problem 29E

The probability that the next household on the list will be contacted but will refuse to cooperate = 0.4712

Explanation of Solution

Given:

P(Household is contacted) = 0.76

P(cooprate) = 0.38

Formula:

Complement rule:

  $P(NotA)=1-P(A)$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Calculation:

  $P\left(Householdrefusesgivencontacted\right)=1-0.38=0.62$

Using multiplication rule,

  $\begin{array}{l}P\left(Householdiscontactedandhouseholdrefusestocooperate\right)\\ =P\left(Householdiscontacted\right)\times P\left(Household\text{ refuses}\text{given }contacted\right)\\ =0.76\times 0.62\\ =0.4712\end{array}$

Hence, the probability that the next household on the list will be contacted but will refuse to cooperate is 0.4712

b)

To determine

To find probability of failing to contact a household or of contacting the household but not getting them to agree to the interview.

Answer to Problem 29E

The probability of failing to contact a household or of contacting the household but not getting them to agree to the interview = 0.7112

Explanation of Solution

Given:

P(Household is contacted) = 0.76

P(cooprate) = 0.38

  $P\left(Householdrefusesgivencontacted\right)=0.62$

Formula:

Complement rule:

  $P(NotA)=1-P(A)$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Calculation:

  $P\left(Failingtocontacted\right)=1-0.76=0.24$

Using multiplication rule,

  $\begin{array}{l}P\left(FailingtocontactHouseholdorcontactingandnotgettingthe\mathrm{int}erview\right)\\ =P\left(Failingtocontacted\right)+P\left(contactinghousehold\right)\times P\left(notgettingthe\mathrm{int}erviewgivencontacted\right)\\ =0.24+0.76\times 0.62\\ =0.7112\end{array}$

Hence, the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview is 0.7112

c)

To determine

To calculate the probability of part b in another way.

Answer to Problem 29E

The probability of failing to contact a household or of contacting the household but not getting them to agree to the interview = 0.7112

Explanation of Solution

Given:

P(Household is contacted) = 0.76

P(cooprate) = 0.38

  $P\left(Householdrefusesgivencontacted\right)=0.62$

Formula:

Complement rule:

  $P(NotA)=1-P(A)$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Calculation:

  $P\left(Failingtocontacted\right)=1-0.76=0.24$

Using multiplication rule,

  $\begin{array}{l}P\left(FailingtocontactHouseholdorcontactingandnotgettingthe\mathrm{int}erview\right)\\ =P(contactinghouseholdandnotgettingthe\mathrm{int}erview)\\ =1-(0.76\times 0.38)\\ =0.7112\end{array}$

Hence, the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview is 0.7112