Collegiate track athletes are subject to random testing for performance enhancing drugs (PED). The test is not completely accurate; an athlete using PED will test positive with probability 0.97, and an athlete who isn't using PED will test negative with probability 0.92.

NCAA race officials used randomized response techniques to estimate the proportion of athletes using PED, while protecting the privacy of the athletes. Each athlete was instructed to provide a simple yes or no response according to the following procedure:

Flip a coin twice, hiding the results from the interviewer.

If the coin came up heads on the first toss, answer the question "Do you use

performance enhancing drugs?"

If the coin came up tails on the first toss, answer the question "Did you flip heads on the second toss?".

• 29% of the athletes responded "yes".

Question: compute the probability that a collegiate athlete is a PED user given they tested positive for PED use