Question 1011771
n = 6
x = 4
p(x) = c(n,x) * p^x * q^(n-x)
p = 4/6 = 2/3
q = 1 - p = 1 - 2/3 = 1/3


p(x) = c(n,x) * p^x * q^(n-x) becomes:


p(4) = c(6,4) * (2/3)^4 * (1/3)^2.


c(n,x) = n! / (x! * (n-x)!)
when n = 6 and x = 4, this becomes:
c(6,4) = 6! / (4! * 2!) = (6*5*4!) / (4!*2!) = (6*5)/2 = 15


p(4) = c(6,4) * (2/3)^4 * (1/3)^2 becomes:
p(4) = 15 * (2/3)^4 * (1/3)^2 = .329218107.


the probability that exactly 4 cases will occur in the next 3 months is equal to .3292 rounded to 4 decimal places.


that's equal to 32.92%.