Question

i have this for homework where I have to come up with the probabilities for each outcome based on a tree diagram. I need to figure out the process of solving these type of problems so i can solve the other ones.

Answer 1

We have the following:

PA = Pet allergy = 0.23

nPA = No Pet allergy = 0.77

P = posivite

N = negative

a) per allergy and test positive

$PA\cdot p=0.23\cdot0.83=0.1909$

The probability is 19.09%

b) pet allergy and test negative

$PA\cdot n=0.23\cdot0.17=0.0391$

The probability is 3.91%

c) tests positive

$\frac{p}{n+p}=\frac{0.83+0.07}{0.83+0.07+0.17+0.93}=0.45$

The probality is 45%

d) no pet alergy and test negative

$n\cdot\text{nPA}=0.93\cdot0.77=0.7161$

The probability is 71.61%