Question: Fred is a beagle “sniffer” dog at a cargo handling depot. Fred is 95% reliable in detecting contraband substances when they are present, and has a probability of only 0.02 of making a mistake when contraband substances are not present.

If the probability that contraband substances are present is 0.01, suppose now we do not know the chance of contraband substances being present. If Fred indicates that contraband substances are present in 5% of cargoes he inspects, what is the probability that a cargo contains contraband substances? (Show your working)