Question

1. At the Bank of California, past data show that 7% of all credit card holders default at some time in their lives. On one recent day, this bank issued 13 credit cards to new customers. Find the probability that of these 13 customers none credit card holders will default.

   	a.	0.0784
   	b.	1.5943
   	c.	0.2910
   	d.	0.3893

Answer 1

The correct option is d. 0.3893 [ANSWER]

Explanation:

We are given that 7% of all credit card holders default at some point 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 7% = 0.07. Thus, we get:

P(a new credit card holder will default) = 0.07

=> P(a new credit card holder will not default) = 1 - P(a new credit card holder will default) = 1 - 0.07 = 0.93

Now, we are given that the bank issued 13 credit cards to new customers (which we can assume to be independent) and we need to find the probability that none of these 13 customers will default on their credit card which is given as follows:

P(none of the 13 customers will default on their credit card) = P(first customer will not default on their credit card)*P(second customer will not default on their credit card)*......*P(13th customer will not default on their credit card)

[Since, all the 13 customers are independent]

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