Stats problem i need help with

Question

The Bank of Hudson Bay reports that 7% of its credit card holders will default at some time in their life. The Moose Factory branch just mailed out 12 new cards today.

1.How many of these new cardholders would you expect to default? What is the standard deviation?
2.What is the likelihood that none of the cardholders will default?
3.What is the likelihood at least one will default?

Answer 1

Hi Bob,

 

1) How many of these new cardholder would you expect to default?

 

I would expect 7% of them to default.  12(.07) = .84

I would expect 1 to default

 

2)  What is the likelihood that none of the cardholder will default?

The probability that any ONE of them defaults is 7%.  So the likelihood that one does not default is 93%.  The likelihood that no one defaults is the likelihood that the first one does not default AND the 2nd does not default AND the 3rd and so on (.93)¹² = .419

 

3) What is the likelihood that at least one will default?

This is the complement of the likelihood that none will default.

1-.419 = .581