Question

The famous cycling race Tour de France has in recent years been plagued with accusations against cyclists for taking steroids. Testing for the presence of steroids is expensive and difficult, partly because these substances occur naturally in the human body and partly because different individuals have different levels than other individuals. It is estimated that about 2% of the racers have taken an illegal steroid. If a cyclist has taken an illegal steroid (labeled S on the tree diagram), the test will yield a positive result 99% of the time. (That means there is a 1% chance of a ‘false negative’ result. If a cyclist has not taken an illegal steroid (labeled S^C on the tree diagram), there is still a 3% chance that the test will return a positive result (a ‘false positive.’) Fill in these probabilities and their complements on the branches of the tree diagram.

a.

0.0198

b.

0.0492

c.

0.99

d.

0.0297

e.

0.03

Answer 1