Answer:
a) 0.00136008
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of any other customer. Thus, the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
9.8% of his customers buy a magazine
This means that ![p = 0.098](https://tex.z-dn.net/?f=p%20%3D%200.098)
What is the probability that exactly 5 out of the first 10 customers buy a magazine?
This is
when
. So
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 5) = C_{10,5}.(0.098)^{5}.(0.902)^{5} = 0.00136008](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B10%2C5%7D.%280.098%29%5E%7B5%7D.%280.902%29%5E%7B5%7D%20%3D%200.00136008)
Thus, the correct answer is given by option A.