# Credit Card Payments: Probability

#### ranish293

##### New member
Hello,

Im having difficulty in solving following problem related to probability, Please anyone provide me with the solution.

The proportion of American Express credit-card holders who pay their credit card bill in full
each month is 23%; the other 77% make only a partial or no payment.

(a) In a random sample of 15 customers, what is the probability that:
i. 4 customers pay their bill in full?
ii. More than 6 customers pay their bill in full?

(b) In a random sample of 17 customers, what is the probability that:
i. 4 customers pay their bill in full?
ii. No more than 3 customers pay their bill in full?

#### Bacterius

##### Well-known member
MHB Math Helper
Re: Probability

Where are you having issues? Do you know about the binomial distribution?

#### ranish293

##### New member

I dont know about binomial distribution, Could you please solve this for me, and explain the procedure.

#### MarkFL

Staff member
...Could you please solve this for me, and explain the procedure.
We don't generally work problems, unless they are posted as challenges, where the OP is expected to already have a complete and correct solution ready to post or if someone brings a problem here from another site.

What we expect (as per rule #11) when someone posts a problem, is for them to show what they have already tried and where they are stuck, or at least post what their thoughts are on how to begin. Then, our helpers may offer suggestions/hints so that the OP can proceed and post feedback or ask for further clarification.

We try to engage the OP as much as possible so that they learn by doing rather than simply have their problems worked for them. While this takes more effort/time on the part of our helpers, this benefits people far more.

Can you state any theorems which you have been given that you think may apply?

edit: I have moved this topic to the Basic Probability and Statistics forum as it involves elementary techniques.

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#### HallsofIvy

##### Well-known member
MHB Math Helper
If each "event" has probability p of happening (so probability 1- p of not happening) then it has probability $$\displaystyle \left(\begin{array}{c}n \\ x \end{array}\right)p^x (1- p)^{n- x}$$ of happening x times out of n trials.
$$\displaystyle \left(\begin{array}{c}n \\ x \end{array} \right)$$ is the "binomial coefficient", $$\displaystyle \frac{n!}{x!(n-x)!}$$.