Following the introduction of the euro, counterfeiters expand their activities. The probability that a euro bill is counterfeit is 0.5%. Retailers are vigilant and install machines at the cash registers to identify counterfeit money. The devices are able to detect a counterfeit euro bill in 95% of cases. In 1% of cases, they record a euro bill as counterfeit that is genuine.

(a) What is the probability of the machines detecting a counterfeit bill?

(b) What is the probability that the money is really counterfeit?