Question

In a large population, 3% of the people are heroin users. A new drug test correctly identifies users 93% of the time and correctly identifies nonusers 90% of the time. Answer the following, showing all work for full credit. a) Draw the probability tree for this scenario. Label the outcomes and indicate all the probabilities on the tree. b) What is the probability that a person who does not use heroin in this population tests positive

Answer 1

Explanation:

From the given information:

3% = 0.03 of the people are heroin users

i.e

non - heroin users = 1 - 0.03 = 0.97

For heroin users,

After testing the new drug,

tested correctly = 0.93 (positive)

tested incorrectly = 1 - 0.93 = 0.07 (negative)

For non-heroine users,

After testing the new drug,

tested correctly = 0.90 (positive)

tested incorrectly = 1 - 0.90 = 0.10 (negative)

a) Therefore, the probability tree diagram can be represented as:

Large population

Heroine users Non-Heroine users

(0.03) (0.97)

tested (+Ve) teste(-ve) tested (-ve) tested (+Ve)

correctly incorrectly correctly incorrectly

(0.93) (0.07) (0.90) (0.10)

b) the probability that a person who does not use heroin in this population tests positive is :

Pr (Non-Heroine users | tested positive ) = 0.10