Question 1201217
p(x) = p^x * q^(n-x) * c(n,x)


the sum of all probabilities needs to be 1.


in your problem:


p = .73
q = 1 - .73 = .27


p(6) = .73^6 * .27^1 * c(7,6) = .2860216877
p(7) = .73^7 * .27^0 * c(7,7) = .1104739852


your solution is the sum of these = .3964956729.


c(n,x) is equal to n! / (x! * (n-x)!)


for example:
c(7,6) is equal to 7! / (6! * 1!) = (7 * 6!) / (6! * 1!) = 7


here's all the probabilities that i calculated using excel.
the total probability is 1 as it should be.


<img src = "http://theo.x10hosting.com/2023/032501.jpg">