Conditional Probability Help (1 Viewer)

[csi]

Please help with the following:

Given:

• 2% professional cyclists have taken an illegal substance in the past 6 months
• The test only produces positive or negative results
• 90% cyclists that have taken an illegal substance in the past 6 months will test positive
• 1% cyclists who did not take any illegal substance in the past 6 months will test positive

1. what is the probability of a positive test? (0.028)
2. what is the probability of a negative test given the cyclist took an illegal substance within the past 6 months? (0.1)
3. what is the probability of a positive test given the cyclist took an illegal substance within the past 6 months? (0.647)

Thanks!

 

[cossine]

Please help with the following:

Given:

• 2% professional cyclists have taken an illegal substance in the past 6 months
• The test only produces positive or negative results
• 90% cyclists that have taken an illegal substance in the past 6 months will test positive
• 1% cyclists who did not take any illegal substance in the past 6 months will test positive

1. what is the probability of a positive test? (0.028)
2. what is the probability of a negative test given the cyclist took an illegal substance within the past 6 months? (0.1)
3. what is the probability of a positive test given the cyclist took an illegal substance within the past 6 months? (0.647)

Thanks!

1. P(Postive_test and not_doing_drug) + P(positive_test and doing_drug)
2. P(negative_test | taken_drug)
3. P(positive_test | taken_drug)

So the two main things too know are the definition of conditional probability and Bayes theorem. Using the definition or theorem you will be able to answer these type of questions. Use the logic based definition of conditional probability. The alternative is the set theory based definition but I presumed you have not studied set theory.

On this site you will find the set theory and logical based definition
https://www.investopedia.com/terms/c/conditional_probability.asp