Find the indicated probability. Round to the nearest thousandth.
-In a batch of 8,000 clock radios 2% are defective. A sample of 11 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective.
What is the probability that the entire batch will be rejected?
A) 0.0909
B) 0.199
C) 0.801
D) 0.0200

Question

Quizplus · Accepted Answer

The probability that at least one of the 11 tested clock radios is defective is the complement of the probability that none of them are defective. 
P(at least one defective) = 1 - P(none defective) 
We can use the formula for probability of a non-defective item in a sample of size n:

P(none defective) = (number of non-defective items in population) / (population size) * (number of non-defective items in reduced sample) / (reduced sample size - 1) * ... * (number of non-defective items in reduced sample) / (reduced sample size - n + 1)

Plugging in the numbers:

P(none defective) = (0.98)^11 = 0.8165

So,

P(at least one defective) = 1 - 0.8165 = 0.1835

Therefore, the probability that the entire batch will be rejected is 0.1835, which rounded to the nearest thousandth is 0.199.

Find the Indicated Probability