I've an interesting question on my hand which I've approach several others but all of them gives me different insights to this probability question.
Here it is,
The incidence of a suspicious transaction in a bank is
1 in 149. They are able to correctly identify a legitimate transaction
92%of the time. However, this bank is also able to correctly pinpoint a suspicious transaction
92%of the time. One day, the bank identify a transaction as suspicious. What is the exact probability of the transaction actually being legitimate?
From my personal point of view, if the question ask for the probability of the transaction actually being legitimate, states that the rate is 148⁄149. The bank is able to correctly identify (which they fail to) a legitimate and suspicious transaction. Therefore, the failure % should be
(8% * 8%) which is
0.08 * 0.08 = 0.0064. Hence, the probability of it actually being legitimate is 148⁄149
* 0.0064 = 0.00636.
However, i asked various people of their opinion and some states that the probability should be just 148⁄149
Therefore, what should be the most probable answer to problems like this.