You are building a system to detect fraudulent card transactions. The first feature that you use is whether the transaction has taken place in the country where the card has been registered (country of registry). Data analysis suggests that 95% of fraudulent transactions do not take place in the country of registry, 98% of the genuine transactions take place in the country of registry, and 1% of transactions overall take place in a country different than the country of registry.

i) What is the probability that a transaction is taking place in a country different than the country of registry?

ii) If a transaction has not taken place in the country of registry, what is the probability that it is fraudulent? What is the decision that one should make for such a transaction? Fraudulent or genuine?

iii) What is the probability that the decision of the classifier is wrong for a transaction that has not taken place in the country of registry?

If possible, please use Baye's Theorem.