1 30of credit card holders carry no mothly balance while 70

1. 30%of credit card holders carry no mothly balance, while 70% do. Of those cardholders carrying a balance, 30% have an annual income $20,000 or less, 40% between $20,001 and $50,000, and 30% over $50,001. Of those cardholders carrying no balance, 20%, 30% and 50% have annual incomes in there three respective categories.

a. What is the probability that a randomly chosen cardholder has annual income $20,000 or less?

b. If the card holder has an annual income that $20,000 or less, what is the probability that he/she carries a balance

Solution

Lets assume that there are 1000 credit card holders.

Number of credit card holders with no monthly balance = 30% of 1000 = 300

Number of credit card holders with monthly balance = 70% of 1000 = 700

Number of credit card holders with monthly balance having an annual income of $20,000 or less = 30% of 700 = 210

Number of credit card holders with monthly balance having an annual income between $20,001 and $50,000 = 40% of 700 = 280

Number of credit card holders with monthly balance having an annual income between over $50,001 = 30% of 700 = 210

Number of credit card holders with no monthly balance having an annual income of $20,000 or less = 20% of 300 =

60

Number of credit card holders with no monthly balance having an annual income between $20,001 and $50,000 = 30% of 300 = 90

Number of credit card holders with no monthly balance having an annual income between over $50,001 = 50% of 300 = 150

Now we will put these values in a table.

a.

P(a cardholder has annual income $20,000 or less) = (210+60)/1000 = 0.27

b.

P(carries a balance | card holder has an annual income of $ 20,000 or less) = 210/(210+60) = 0.78