Question

aaron is required to be tested for covid-19 once per week for the next six weeks, for his job. the false positive rate for covid lab tests is assumed to be .01. using binomial probability, and assuming he does not actually become infected, what is the probability that aaron gets at least one false positive test during this time?

Answer 1

The probability that Aaron gets at least one false positive test during the six weeks is 0.0490029916.

Step-by-step explanation:

To calculate the probability that Aaron gets at least one false positive test during the six weeks, we can use the complement rule and subtract the probability of getting zero false positive tests from 1. The probability of getting a false positive in one week is 0.01.

Since Aaron is tested once per week for six weeks, we can use the binomial probability formula to calculate the probability of getting zero false positive tests:

P(X = 0) = (n choose x) * (p^x) * ((1-p)^(n-x))

where n is the number of trials, x is the number of successes (in this case, zero false positive tests), and p is the probability of success (0.01).

Using the formula, we have:

P(X = 0) = (6 choose 0) * (0.01^0) * ((1-0.01)^(6-0))

= 0.9509970084

Now, we can find the probability of getting at least one false positive test by subtracting the probability of getting zero false positive tests from 1:

P(at least one false positive) = 1 - P(X = 0)

= 1 - 0.9509970084

= 0.0490029916.