Find the indicated probability.
-In a batch of 8000 clock radios 6% are defective. A sample of 12 clock radios is randomly selected without replacement from the 8000 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)0.524
B)0.0600
C)0.0833
D)0.476

Question

Quizplus · Accepted Answer

To find the probability that the entire batch will be rejected, we first calculate the probability that none of the 12 radios tested is defective, and then subtract that probability from 1. There are 8000 radios in total, with 6% defective, so 480 are defective (6% of 8000) and 7520 are not defective. The probability that the first radio is not defective is 7520/8000, the second is 7519/7999, and so on, down to 7509/7989 for the twelfth radio. The probability that all 12 tested radios are not defective is the product of these probabilities. The probability that at least one is defective (and thus the batch is rejected) is 1 minus this product. Calculating this gives a probability greater than 0.5, making A the correct choice.

Find the Indicated Probability