Hi, there--

THE PROBLEM:
A box contains 90 good items and 10 defective items. Find the probability that a
sample of 10 items has no defective items.

A SOLUTION:
This situation can be modeled by the Binomial Probability Distribution, X~Binomial (n, p)
where
X is the random variable
n is the sample size = 10 items
k is the number of successes you are interested = 10
p is the probability of success (selecting a good item) = 90/100 = 0.9

The equation for finding the probability is

P(X=k) = [nCk] * [p^k] * [(1-p)^(n-k)]

nCk is a combination, the number of ways to choose k items from a set of n items. In your
problem, we have 10C10, the number of ways to choose 10 good items from a sample of 10 
items.

Therefore the probability of the all ten items in the sample will be good is

P(X=10) = [10C10] * [(0.9)^10] * [(0.1)^0]
P(X=10) = (1) * (0.34868) * (1)
P(X=10) = 0.34868

Therefore, the probability that a sample of ten items has no defective items is 0.34868.


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com