Question

At the Bank of California, past data show that 19% of all credit card holders default at some time in their lives. On one recent day, this bank issued 11 credit cards to new customers. Find the probability that of these 11 customers at most 3 credit card holders will default.

Answer 1

We are given that at Bank of California, 19% of all credit card holders default at some time in their lives. It means that the probability that a randomly selected new credit card holder will default at some point in their life is equal to 19% = 0.19.

Now, let X denote the number of customers who will default on their credit cards, out of the 11 new credit card customers.

Since, there is a fixed number of new credit card customers (equal to 11), each credit card customer has two outcomes (defaulting or not defaulting) and each credit card customer defaults on their credit card with probability 0.19 independent of other customers, thus we can conclude that:
X ~ Binomial(n = 11, p = 0.19) and the probability mass function of X is given by:

Now, the probability that at most 3 credit card holders will default on their credit cards is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.