LabTech is a company that manufactures microscopes and other laboratory instruments . On occasion, one of the microscopes is def
ective when it comes off of the production line. The probability that a microscope is defective is 0.17%. Find the probability that one of the first 50 microscopes is defective .
The required probability will be found by using the Binomial Distribution which fits the case of n independent events each with a probability of success equal to p with k successes.
The PMF (Probability Mass Function) is
Where
LabTech states that the probability that a microscope is defective is 0.17%, p=0.0017, q=0.9983. We need to know the probability that k=1 microscope is defective out of a set of n=50 of them. We now apply the formula
Which means that there is a 7.82% of probability to get 1 defective microscope out of the first 50