Baye's Rule allows us to estimate the probability of an inductive conclusion being true, given the observed evidence. We make inductive conclusions all the time, and it's interesting to see how the objective probability generated by Baye's Rule can apply to everyday scenarios. Imagine you are single (if you aren't in real life) and standing in line at the coffee shop and strike up a nice conversation with the attractive customer standing in line next to you. They seem to be enjoying the conversation and even have some common interests. This nice conversation ("evidence") makes you think they might be receptive to going on a date with you ("hypothesis"). The posterior probability, P(HIE), is the probability of the hypothesis being true given the evidence is true. In this example, P(HIE) is the probability that the person would go on a date with you given you had this nice conversation with them. a. In this example, what is P(H)? Remember, this stands for the probability of the hypothesis being true without any additional evidence. (3 points) b. In this example, what is P(E|H)? Remember, this stands for the probability of the evidence being true given the hypothesis is true. (3 points) C. 2 In this example, what is P(E|~H)? Remember, this stands for the probability of the evidence being true given the hypothesis is NOT true. (3 points) d. In this example, what is P(H)? Remember, this stands for the probability the hypothesis is NOT true without any additional evidence. (3 points) e. What probability do you think would be a good guess for P(H)? In a sentence or two, explain why. (4 points) f. What probability do you think would be a good guess for P(E|H)? In a sentence or two, explain why. (4 points) g. What probability do you think would be a good guess for P(E|~H)? In a sentence or two, explain why. (4 points)