MHB Credit Card Payments: Probability

AI Thread Summary
The discussion revolves around calculating probabilities related to American Express credit card holders who pay their bills in full. The initial poster seeks help with specific probability questions involving a binomial distribution, specifically for samples of 15 and 17 customers. Respondents emphasize the importance of understanding the binomial distribution and suggest that the poster should demonstrate their attempts at solving the problem before seeking direct solutions. They explain the binomial probability formula, highlighting the need for the poster to engage with the material for better learning. The conversation underscores a focus on educational support rather than simply providing answers.
ranish293
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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?
 
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Re: Probability

Where are you having issues? Do you know about the binomial distribution?
 
Thanks Bacterius for your reply.

I don't know about binomial distribution, Could you please solve this for me, and explain the procedure.
 
ranish293 said:
...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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ranish293 said:
Thanks Bacterius for your reply.

I don't know about binomial distribution, Could you please solve this for me, and explain the procedure.
It's very strange that you would be given a problem like this- which is a "binomial distribution" problem if you have never learned about it.

If each "event" has probability p of happening (so probability 1- p of not happening) then it has probability $$\left(\begin{array}{c}n \\ x \end{array}\right)p^x (1- p)^{n- x}$$ of happening x times out of n trials.

In problem (ai), for example, p= 0.23, n= 15, and x= 4.

$$\left(\begin{array}{c}n \\ x \end{array} \right)$$ is the "binomial coefficient", $$\frac{n!}{x!(n-x)!}$$.
 
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