SOLUTION: I need some help with this question. I can't figure out how to solve it. Any help would be great, thank you. In a binomial situation, n = 4 and p = 0.24. Determine the probabili

Click here to see ALL problems on Probability-and-statistics

Question 1118171: I need some help with this question. I can't figure out how to solve it. Any help would be great, thank you.
In a binomial situation, n = 4 and p = 0.24. Determine the probabilities of the following events using the binomial formula. (Round the final answers to 4 decimal places.)

a. x = 2

Probability :

b. x = 3

Probability :

c. x ≥ 2

Probability :

d. x < 3

Probability :
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the binomial probability formula is:

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

c(n,x) is the number of ways you can get a set of x elements out of a set of n elements when order of the elements within each set of x elements is not important.

that formula is c(n,x) = n! / (x! * (n-x)!).

p = .24
q = 1 - .24 = .76
n = 4
x = 0 to 4

p(x = 2) would be c(4,2) * .24^2 * .76^2 = 0.19961856
p(x = 3) would be c(4,2) * .24^3 * .76^1 = 0.04202496
p(x >= 2) would be p(x = 2) + p(x = 3) + p(x = 4) = 0.24496128
p(x < 3) would be p(x = 0) + p(x = 1) + p(x = 2) = 0.95465728

the complete analysis is shown in the following spreadsheet.

the sum of all probabilities is equal to 1, as it should be.