SOLUTION: Among eighteen computers in some store, six have defects. Five randomly selected com- puters are bought for the university lab. Compute the probability that all five computers ha

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

Question 1034119: Among eighteen computers in some store, six have defects. Five randomly selected com-
puters are bought for the university lab. Compute the probability that all five computers
have no defects.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
18 computers with 6 having defects.
probability of picking a computer that has a defect is 6/18 = 1/3.
probability of picking a computer that doesn't have a defect is 12/18 = 2/3.

the probability that all 5 computers have no defect is (2/3)^5 = .1316872428.

the formula used is p(x) = c(n,x) * p^x * q^(n-x)

c(n,x) is the combination formula of getting x out of n.
x is the number of computers that are not defective.
n-x is the number of computers that are defective.
p is the probability that a computer is not defective.
q is the probability that a computer is defective.

in your problem:
n = 5 because that's the number of computers you are drawing from the population of 18.
x is 5 because that's the number of computes that are expected to not be defective.
n-x is 0 because that's the number of computers that are expected to be defective.
p is the probability that a computer is not defective = 12/18 = 2/3.
q is the probability that a computer is defective = 6/18 = 1/3.

the formula, applied to your problem becomes:

p(5) = c(5,5) * (2/3)^5 * (1/3)^0 = 1 * (2/3)^5 * 1 = (2/3)^5 = .1316872428.

the complete list of probabilities is shown below.
the sum of the probabilities is 1 as it should be.