SOLUTION: If new cases of West Nile Disease in New England are occurring at a rate of about 2 per month, then what�s the probability that exactly 4 cases will occur in the next 3 months?

Question 1011771: If new cases of West Nile Disease in New England are occurring at a rate of about 2 per month, then what�s the probability that exactly 4 cases will occur in the next 3 months?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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%.

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