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If a company is testing its 200 employees for drugs and they are being drug screened with a test that has a 98.5% chance of being accurate. What is the probability that at least one person will be let go for taking drugs when they are clean?

User DAVL
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1 Answer

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Final answer:

The probability that at least one person will be let go for taking drugs when they are clean is approximately 0.954, or 95.4%.

Step-by-step explanation:

To find the probability that at least one person will be let go for taking drugs when they are clean, we can use the complement rule.

The complement rule states that the probability of an event not happening is equal to 1 minus the probability of the event happening.

In this case, the probability of at least one person being let go for taking drugs when they are clean is equal to 1 minus the probability that all 200 employees pass the drug test.

Since the test has a 98.5% chance of being accurate, the probability that an employee will pass the test is 0.985.

Therefore, the probability of all 200 employees passing the test is 0.985^200.

Now, we can calculate the probability of at least one person being let go:

Probability of at least one person being let go = 1 - Probability that all 200 employees pass the test

= 1 - 0.985^200

= 0.954

So, the probability that at least one person will be let go for taking drugs when they are clean is approximately 0.954, or 95.4%.

User Albert Veli
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