select the correct answer. suppose you have data that shows that 12% of athletes test positive for steroids…

select the correct answer. suppose you have data that shows that 12% of athletes test positive for steroids. you also know that 11% of athletes test positive for steroids and actually use steroids. what is the probability that an athlete uses steroids, given that he tests positive?\na. 0.37\nb. 0.43\nc. 0.51\nd. 0.67\ne. 0.92

select the correct answer. suppose you have data that shows that 12% of athletes test positive for steroids. you also know that 11% of athletes test positive for steroids and actually use steroids. what is the probability that an athlete uses steroids, given that he tests positive?\na. 0.37\nb. 0.43\nc. 0.51\nd. 0.67\ne. 0.92

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that an athlete uses steroids and $B$ be the event that an athlete tests positive for steroids.

Step2: Identify given probabilities

We are given that $P(B) = 0.12$ (probability of testing positive) and $P(A\cap B)=0.11$ (probability of testing positive and using steroids).

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.11}{0.12}\approx0.92$.

Answer:

E. 0.92