Tree diagrams, conditional probability, false positives
biosecurity
At an international airport, 2% of arriving bags contain undeclared risk goods (e.g. fruit or meat). A biosecurity detector dog indicates (sits beside) 90% of bags that contain risk goods and 5% of bags that do not.
Figure 1 shows a probability tree for one randomly chosen bag; some branch probabilities are shown as ?.
Probability tree: first branches split bags into risk goods (0.02) and no risk goods (?); each then splits into dog indicates or does not indicate, with 0.90 and ? for risk bags and 0.05 and ? for clean bags.Facts you may need
(a)
Use Figure 1 to find the probability that the dog indicates a randomly chosen bag.
(b)
Given the dog indicates a bag, find the probability it contains risk goods. Interpret this for officers.
(c)
Out of 10 000 bags, how many bags with risk goods would the dog miss? Use this and P(risk∣no indication) to evaluate relying on dogs alone.
