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

Step-by-step 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

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,