Question

In: Computer Science

For the year 2017, Fred Friendly completed a total of 80 returns. He developed the following table summarizing the relationship

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.

Dependents Refund 3 or more 10 Total 20 20 40 50 30 80 20 10 30 Yes No Total 10 이은

 

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?

Solutions

Expert Solution

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.

 

 

Junaid answered 2 years ago
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