Strep Throat Test

You are a physician. You think it is quite likely that one of your patients has strep throat, but you aren't sure.

You estimate the probability of the patient having strep throat is 60%.

You take some swabs from the patient's throat and send them to a lab for testing. The test is not perfect.

If the patient has strep throat, then, 80% of the time, the lab says "Positive," but 20% of the time it says, "Negative."

If the patient does not have strep throat, then, 90% of the time, the lab says "Negative," but 10% of the time it says, "Positive."

You send five successive swabs to the lab, from the same patient. You get back these results, in order:

Positive, Negative, Positive, Negative

Compute the probability that the patient has strep throat