Microprocessing chips are randomly sampled one
by one from a large population, and tested to determine
if they are acceptable for a certain application.
Ninety percent of the chips in the population are
acceptable.
To begin, we need to find the probability of a randomly sampled chip being acceptable. We are given that 90% of the chips in the population are acceptable.
1. Calculate the probability of an acceptable chip:
Probability(acceptable chip) = 90% = 0.90
Now let's move on to answering the specific questions you might have based on this information:
1. What is the probability that the first two chips sampled are both acceptable?
To find the probability that two events both occur, we multiply their individual probabilities. In this case, we want to find the probability of selecting an acceptable chip twice in a row. Since each sampling is independent (the outcome of one chip does not affect the outcome of another), we can multiply the probabilities.
Probability(acceptable chip on first sampling) = 0.90
Probability(acceptable chip on second sampling) = 0.90
Probability(acceptable chip on first sampling and on second sampling) = (0.90) * (0.90) = 0.81
Therefore, the probability that the first two chips sampled are both acceptable is 0.81 or 81%.
2. What is the probability that at least one of the first three chips sampled is unacceptable?
To find the probability of an event occurring at least once, we can find the complement of the event not occurring. In this case, we want to find the probability that none of the first three chips are acceptable and then subtract that from 1 (since the sum of the probabilities of all possible outcomes must equal 1).
Probability(unacceptable chip on first sampling) = 1 - Probability(acceptable chip on first sampling) = 1 - 0.90 = 0.10
Probability(unacceptable chip on first sampling and on second sampling and on third sampling) = (0.10) * (0.10) * (0.10) = 0.001
Probability(at least one unacceptable chip in the first three sample) = 1 - Probability(no unacceptable chip in the first three samples) = 1 - 0.001 = 0.999
Therefore, the probability that at least one of the first three chips sampled is unacceptable is 0.999 or 99.9%.