Question 1205454: Please help me solve
A binomial experiment has the given number of trials and the given success probability, n=8 p=0.1
P
Part 1 of 3
(a)Determine the probability . Round the answer to at least three decimal places.
p(1)=
Found 2 solutions by math_tutor2020, Theo:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
P(x) = (n C x)*(p^x)*(1-p)^(n-x)
P(x) = (8 C x)*(0.1^x)*(1-0.1)^(8-x)
P(1) = (8 C 1)*(0.1^1)*(1-0.1)^(8-1)
P(1) = 8*(0.1^1)*(1-0.1)^(8-1)
P(1) = 0.38263752
P(1) = 0.383
The nCx refers to the nCr combination formula.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! binomial distribution probability formula is:
p(x) = p^x * q^(n-x) * c(n,x)
n = the number of total probabilities.
x = 0 to n
c(n,x) = n! / (x! * (n-x)!)
in your problem:
n = 8
p = .1
x = 0 to 8
q = 1-p = .9
you are solving for p(0) to p(8)..
the sum of all probabilities needs to be equal to 1.
here's the probabilities that i solved using excel to do the calculations.
for example:
calculations for n = 8 and x = 3 are shown below:
p(3) = .1^3 * .9^5 * c(8,5) = .03306744.
the breakdown of the piece parts is as follows:
.1^3 = .001
.9^5 = .59049
c(8,3) = 8! / (3! * 5!) = (8 * 7 * 6 * 5!) / (3 * 2 * 1 * 5!)
the 5! in the numerator and denominator cancel out and you are left with:
(8,3) = (8 * 7 * 6) / (3 * 2 * 1)
8 / 2 = 4 and 6 / 3 = 2, so you are left with:
c(8,3) = (4 * 7 * 2) which is equal to 56.
you have:
.1^3 = .001
.9^5 = .59049
c(8,3) = 56
you get p(3) = .1^3 * .9^5 * c(8,3) which becomes p(3) = .001 * .59049 * 56 which gets you:
p(3) = .03306744 as shown for x = 3 in the excel printout.
your solution is p(1) = .1^1 * .9^7 * c(8,1) = 0.38263752.
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