Question

A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like

Answer 1

Answer:

The probability tree is;

                            0.95        $(+)$

                   $(S)$

          0.1              0.05        $(-)$

[  P  ]

          0.9             0.15          $(+)$                                                        

                  $(S_{no})$    

                             0.85         $(-)$        

Step-by-step explanation:

Given the data in the question;

10% of the rugby team members use steroids

so Probability of using steroid; P( use steroid ) = 10% = 0.10

Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90

Since the test show positive for an athlete who uses steroids, 95% of the time.

Probability of using steroids and testing positive = 95% = 0.95

Probability of using steroids and testing Negative = 1 - 0.95 = 0.05

Also from the test, 15% of all steroid-free individuals also test positive.

so

Probability of not using steroids and testing positive = 15% = 0.15

Probability of not using steroids and testing negative = 1 - 0.15 = 0.85

To set up the probability tree, Let;

$(S)$ represent steroid use

$(S_{no})$ represent no steroid use

$(+)$ represent test positive

$(-)$ represent test negative

so we have;

                            0.95        $(+)$

                   $(S)$

          0.1              0.05        $(-)$

[  P  ]

          0.9             0.15          $(+)$                                                        

                  $(S_{no})$    

                             0.85         $(-)$