A country has two teams of weightlifters; in one, 80% use steroids regularly, and in the other, only 20% use them. The head coach flips a coin and selects the team for the international meet. At the venue, if one lifter was selected at random for the drug test and found positive, what is the probability that the team is the steroid one?
We will use the base form of Bayes’ theorem – the relationship between conditional and joint probabilities.
P(S/T) = P(S & T) / P(T)
S – it is a steroid team
T – tested member used steroid
C – it is a clean team
P(S & T) = P(S) x P(T|S) = 0.5 (coin toss) x 0.8 (chance of using steroids, given he is from the steroid team) = 0.4
P(T) = P(S) x P(T|S) + P(C) x P(T|C) = 0.5 x 0.8 + 0.5 x 0.2 = 0.5
P(S/T) = 0.4/0.5 = 0.8
The probability that the team is the steroid one is 80%
