Question

When a test for steroids is given to soccer players, 98% of the players taking steroids test positive and 12% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids. What is the probability that a soccer player who tests positive takes steroids?

Answer 1

Answer:

P = 0.300 or 30%

Step-by-step explanation:

There are two possibilities for a player to test positive:

1-) He does not take steroids (95%) with a 12% chance of testing positive:

P= 0.95 x 0.12

2-) He does take steroids (5%) with a 98% chance of testing positive:

P= 0.05 x 0.98

So the probability that a player tests positive is:

P = 0.95 x 0.12 + 0.05 x 0.98 =0.163

Therefore, the probability that a soccer player who tests positive takes steroids is:

$P= \frac{0.05 * 0.98 }{0.163}\\P=0.300$