(b) This part asks you to calculate the conclusions Nate draws from seeing Kimayabe pleasant four times.

i. Calculate the probability with which Nate thinks Kimaya is pleasant fourt imes in a row if she is mean.

ii. Calculate the probability with which Nate thinks Kimaya is pleasant four times in a row if she is average.

iii. Calculate the probability with which Nate thinks Kimaya is pleasant four times in a row if she is nice.

iv. Based on the answers to the previous parts, calculate the overall probability that Nate thinks Kimaya is pleasant four times in a row.
v. Apply Bayes’ rule and calculate the probability with which Nate thinks Kimaya is nice conditional on the fact that she was pleasant four times in a row.

(c) Explain the general intuition behind the difference in your final answers to parts(a) and (b).

(d) Nate decides that he is not yet sure whether Kimaya is nice, so that he should meet Kimaya regularly to find out. After a while, he meets her nineteen more times. Before the first of these nineteen meetings takes place, the balls in his imaginary urn are replenished (and they are not replenished again for the duration of these nineteen meetings). This time Kimaya is pleasant twelve times and not pleasant seven times. Does this increase or decrease Nate’s confidence that Kimaya is nice?Should it? Explain the intuition. [Hint: Although you can answer this question using Bayes’ rule, there is a simpler way to do it. Namely, you can ask whether a mean, average, or nice Kimaya is most likely to be pleasant twelve times and not pleasant seven times, and what Nate thinks about these likelihoods.]