Law of Total Probability

Dating apps allow us to look a person's profile (or picture) and decide whether we'd like to date them (swipe right) or not {swipe left). Let us treat this like a hypothesis test, with the null hypothesis being that you don't want to date them. Then the swipe right decision is a positive result (rejecting the null) and the swipe left decision is a negative result {not rejecting the null). Suppose you think you're pretty good at deciding who you want to date, and you think that your sensitivity is 80% and your specicity is 66%. 4. if you go through the profiles of 200 people in a population where you expect 25% of the population to be dateable, how many times can you expect to swipe right? Hint: multiply the probability by the number of people to nd out the expected number of swipes. 5. If instead the population had only 5% dateable individuals, how many times can you expect to swipe right? 6. Suppose you swipe right on a person from the 25% dateable population and go on a date. What's the probability that it's a good one (this is a person you actually want to date)? 7. Suppose you swipe right on a person from the 5% dateable population and go on a date. What's the probability that it's a good one (this is a person you actually want to date)