Question

For the year 2017, Fred Friendly completed a total of 80 returns. He developed the following table summarizing the relationship between number of dependents and whether or not the client received a refund.

 

a. What is the name given to this table?
b. What is the probability of selecting a client who received a refund?
c. What is the probability of selecting a client who received a refund or had one dependent?
d. Given that the client received a refund, what is the probability he or she had one dependent?

e. What is the probability of selecting a client who did not receive a refund and had one dependent?

Answer 1

a.

The name of the given table is contingency table. The given table summarizes the relationship between number of dependents or whether or not the client received a refund.

 

b.

The probability of selecting a client who received a refund is,

50/80 = 0.625

 

The required answer is 0.625.

 

c.

The probability of selecting a client who received a refund or had one dependent is,

P(Refund or One dependent) = P(Refund) + P(One dependent) – (Refund and One Dependent)

                                                    = 50/80 + 30/80 – 20/80

                                                   = 0.75

 

The required answer is 0.75.

 

d.

Given that the client received a refund, the probability that he or she had one dependent is,

P(One dependent | refund) = P(One dependent and Refund)/P(Refund)

                                                  = (20/80)/(30/80)

                                                  = 0.67

 

The required answer is 0.67.

 

e.

The probability of selecting a client who did not receive a refund and had one dependent is,

P(Did not receive a Refund and One dependent) = 10/80

                                                                                      = 0.125

 

The required answer is 0.125.