Answer:
a) 0.4352
b) 0.5165
c) 0.0813
Step-by-step explanation:
In this problem we have 3 defective parts scattered among 15 parts.
We are going to select 3 out of 15 without replacement, so the situation can be modeled with the Hypergeometric distribution.
If X is the random variable that measures the number of defective parts in a sample of 3, the probability of selecting exactly k defective parts out of 15 would be given by
a) what is the probability that the inspector finds exactly one nonconforming part?
Replacing k with 1 in our previous formula, we get
b) what is the probability that the inspector finds at least one nonconforming part?
This would be P(X=1)+P(X=2)+P(X=3) = 1 - P(X=0).
so 1 - P(X=0) = 1 - 0.4835 = 0.5165
c) what is the probability that the inspector finds at least two nonconforming part?
P(X=2) + P(X=3) = 1 - (P(X=0) + P(X=1)) = 1 - (0.4835 + 0.4352) =
= 1 - 0.9187 = 0.0813
