See attached.

A matchmaking site came up with a test to help single men identify a suitable partner. The site would screen its database of eligible women and correctly identify a worthy partner 95% of the time. It is a very accurate screening. The site does make mistakes, however, in the form of false positives. In fact, 1 in 100 would be incorrectly labelled as a suitable partner. There are two measures of the effectiveness of a test like this. The sensitivity of a test (TPR or true positive rate) is the probability that the test result is positive given that an individual is a suitable partner. The specicity (TNR or true negative rate) is the probability that the test result is negative given that an individual is not a suitable partner. Therefore, a good test would have TPR and TNR values close to one. a) [2 marks] Let A be the event \"participant passes screening\" and B be the event \"participant is a suitable partner.\" Dene the sensitivity and specicity in terms of the probability function P(-) and the events A and B. b) [4 marks] Find the probability that a randomly selected matchmaking site member passes the screening. c) [2 marks] Find the probability that a matchmaking site member is a suitable partner given that they passed the screening