Question 1183756
the probability of a set being defective is 6/50 = .12.
the probability of a wet not being defective is 1 - .12 = .88


you select 5 of the 50 at random.


the formula to use is p(x) = p^x * q^(n-x) * c(n,x).
p is the probability of the set being defective.
q is the probability of the set not being defective.
n is equal to 5.
x is equal to 0 to 5.
c(n,x) is equal to n! / (x! * (n-x)!).


you want the probability that exactly 2 of the 5 sets selected at random are defective.


p(2) = .12^2 * .88^(5-2) * c(5,2) = .12^2 * .88^3 * c(5,2) = .12^2 * .88^3 * 10 = .098131968.


that should be your answer.


all the probabilities are shown below:


<img src = "http://theo.x10hosting.com/2021/082201.jpg"


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


probability of exactly 2 defective sets is p(2) = .098131968, which is equal to .098132 when rounded to 6 decimal digits.