Bayes Theorem probability of steroids

In summary, using Bayes Theorem, we can calculate that there is a 91% chance that a player who tests positive for steroids actually takes steroids. This is based on the given information that 5% of soccer players use steroids and 98% of players who take steroids test positive, while only 0.5% of non-steroid users test positive. This is a plausible answer based on the number of people tested and the percentage of players who use steroids.
  • #1
SammC
17
0

Homework Statement


When the test for steroids is given to soccer players, 98% of players taking steroids test positive and 0.5% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids, what is the probability that a player who tests positive takes steroids.


2. Homework Equations and attempt at solution
p: tests positive
s: uses steroids

pr(s) = .05
pr(P|S) = .98

inclusion exclusion pr(p) = Pr(P|S)*Pr(S) + Pr(P|not S) * Pr(not S) = .98*.5 + .005 *.95 = .05375

Bayes Theorem: [Pr(S | P) = Pr(P | S) * Pr(S)]/Pr(p)

plugging in...
Pr(S | P) = .91

My question: Is 91% a plausible answer to this problem? Its the first one I've ever done using Bayes rule.
 
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  • #2
Imagine that there are 100000 people tested. 5% of them, 5000, use steroids, the other 100000- 5000= 95000 do not. Of those 5000 who use steroids, 98%= 4900 test positive. Of the 95000 who do not use steriods, .5% of them= 475 also test positive.

So you have a pool of 4900+ 475= 5375 who test positive and 4900 of those take steroids: 4900/5375= 0.91. Yes, 91% is a plausible answer.
 
  • #3
Thanks Much
 

What is Bayes Theorem and how does it relate to steroids?

Bayes Theorem is a mathematical formula that calculates the probability of an event occurring based on prior knowledge or information. In the context of steroids, Bayes Theorem can be used to determine the probability of an athlete using steroids based on various factors such as drug testing results, physical appearance, and performance.

How accurate is Bayes Theorem in predicting steroid use?

The accuracy of Bayes Theorem in predicting steroid use depends on the quality and reliability of the data used to calculate the probabilities. If the data is accurate and comprehensive, the predictions can be highly accurate. However, if the data is incomplete or biased, the predictions may not be as reliable.

Can Bayes Theorem be used to identify specific steroids used by an athlete?

Bayes Theorem can be used to calculate the probability of an athlete using steroids in general, but it cannot identify specific steroids. To determine which steroids an athlete may be using, additional information and testing would be needed.

What are some limitations of using Bayes Theorem in relation to steroids?

One limitation of using Bayes Theorem for predicting steroid use is that it relies on prior information and may not account for new or emerging steroids. It also assumes that the data used is accurate and representative of the population being studied. Additionally, Bayes Theorem does not take into account individual differences and can only provide a probability, not a definite answer.

How can Bayes Theorem be used in anti-doping efforts?

Bayes Theorem can be used to analyze data from drug testing and other factors to identify athletes who are more likely to be using steroids. This can help anti-doping organizations target their testing efforts and improve the effectiveness of their anti-doping strategies.

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