Question

The Easy Credit Company report the following table representing a breakdown of customers accounting to the amount they owe and whether a cash advance has been made. An auditor randomly selects one of the accounts.

Accounts owned by Customers	Cash Advantage
	Yes	No
$0 – 199.99	245	2890
$200 – 399.99	380	1,700
$400 – 599.99	500	1,425
$600 – 799.99	415	940
$800 to 999.99	260	480
$1000 or more	290	475
Total Customers	2,090	7,910

Show your work!

1. What is the probability that a customer received a cash advance?
2. What is the probability that a customer owed less than $200 and received a cash advance?
3. What is the probability that a customer owed less than $200 or received a cash advance?
4. Given that the customer-owned $1000 or more, what is the probability that the customer received a cash advance?
5. Are the events "receiving a cash advance" and "owning $1000 or more" independent? Explain why or why not.

Answer 1

Amounts owed by customers	Cash Advance		Total
	Yes	No
$0-199.99	245	2.890	3,135
$200-399.99	380	1,700	2,080
$400-599.99	500	1,425	1,925
$600-799.99	415	940	1,355
$800-999.99	260	480	740
$1,000 or more	290	475	765
Total Customers	2,090	7,910	10,000

The joint probability table is given below:

Amounts owed by customers	Cash Advance		Total
	Yes	No
$0-199.99	245/10000=0.0245	2890/10000=0.289	3135/10000=0.3135
$200-399.99	380/10000=0.038	1700/10000=0.17	2080/10000=0.208
$400-599.99	500/10000=0.05	1425/10000=0.1425	1925/10000=0.1925
$600-799.99	415/10000=0.0415	940/10000=0.094	1355/10000=0.1355
$800-999.99	260/10000=0.026	480/10000=0.048	740/10000=0.074
$1000 OR MORE	290/10000=0.029	475/10000=0.0475	765/10000=0.0765
TOTAL CUSTOMERS	2090/10000=0.209	7910/10000=0.791	1

1. Find the probability of a customer received a cash advance. From the joint probability table, the probability corresponding with customer received cash advance is 0.209.Thus, the probability of a customer received a cash advance is 0.209

2. Find the probability of customer owed less than $200 and received a cash advance. From the joint probability table, the probability corresponding with customer owed less than $200 and received cash advance is 0.0245.Thus, the probability of customer owed less than $200 and received a cash advance is 0.0245

3. Find the probability of customer owned less than $200 or received a cash advance. Define the events: C1: Customer received cash advance. C2: Customer owed less than $200. The formula for P(C1 U C2) is given as fallows   P(C1 U C2)=P(C1)+P(C2) - P(C1 n C2). Substitute 0.3135 for P(C1), 0.209 for P(C2) and 0.0245 for P(C1 nC2) in above formula.

Therefore, P(C1 U C2)=0.3135 +0.209 -0.0245 = 0.498 Thus, probability of customer owed less than $200 or received a cash advance is 0.498)

4. Find probability of customer owned $1,000 or more, given that customer received cash advance. Define the events:

C1: Customer received cash advance.

C3: Customer owed $1,000 or more

Formula for probability of customer owed $1,000 or more, given that customer received cash advance is given below: P(C3 | C1) = P(C3 and C1) / P(C1) From probability distribution table, value of P(C3 and C1) is 0.029 and value of P(C1) is 0.209. Therefore, P(C3 | C1)= P(C3 and C1)/P(C1)= 0.029/0.209 = 0.1388 Thus, probability of customer owed $1,000 or more, given that customer received cash advance is 0.1388