The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. the firm is requested to send 3 employees who have positive indications of asbestos on to a medical center for further testing. if 60% of the employees have positive indications of asbestos in their lungs, find the probability that 11 employees must be tested in order to find 3 positives?

So then the probability that 11 employees must be tested in order to find 3 positives is 0.00637

Step-by-step explanation:

Previous concepts

A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".

And the probability mass function is given by:

Where r-1 represent the number successes after the x-1 trials and p is the probability of a success on any given trial.

Solution to the problem

Let X the random variable that represent the number of trials on which the third employee has founded with a positive result of asbestos.

For this case the random variable Y follows a negative binomial distribution given by:

And we want to find the probability P(X=11) and if we replace in the mass function we got:

So then the probability that 11 employees must be tested in order to find 3 positives is 0.00637

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