Question

suppose that 10,000 students at a university were all tested with this saliva test and that, in truth, 100 of them were infected. further, suppose the false positive and false negative rates were actually both 1 in 100 for this group. if someone tests positive, what is the probability (as a decimal) that he or she is infected?

Answer 1

To find the probability that someone who tests positive is infected, we can use Bayes' theorem.

By substituting the given values into the formula, we find that the probability is approximately 0.5 or 50%.

Step-by-step explanation:

Let's define the events:

• A: Student is infected
• B: Student tests positive

We are given the following probabilities:

• P(A) = 100/10000 = 0.01
• P(B|A) = 1/100 = 0.01 (false negative rate)
• P(B|A') = 1/100 (false positive rate)

By Bayes' theorem, the probability that a student is infected given that they test positive is:

P(A|B) = (P(B|A) * P(A)) / (P(B|A) * P(A) + P(B|A') * P(A'))

Substituting the values, we get:

P(A|B) = (0.01 * 0.01) / (0.01 * 0.01 + 0.01 * 0.99)

Simplifying, we find that the probability is approximately 0.5 or 50%.