Probability question
Athletes who have used banned substances will test negative 1/4 of the time. Athletes who have not used banned substances will return a false positive 1/8 of the time. If a third of athletes have used banned substances, what is the probability that an athlete testing positive has actually used banned substances?
Came across this question but can't get my head around how to get the correct answer (3/4). Can anyone help? I believe it is at GCSE level but I'm not too sure, it may require some S1 knowledge
Came across this question but can't get my head around how to get the correct answer (3/4). Can anyone help? I believe it is at GCSE level but I'm not too sure, it may require some S1 knowledge
Probably the easiest approach to this question is to consider a group of 12 athletes and to construct a tree diagram. The first level of the tree divides the 12 into the number you would expect to have used banned substances and the number you would expect to be clean. At the second level of the tree, the substance users are divided into true positives and false negatives, while the clean athletes are divided into false positives and true negatives, according to the given probabilities in both cases. You then have to look at all the positive results and determine what proportion of them you would expect to be true positives.
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