Question

Recall the cookie problem from lecture. We have two bowls, Bowl 1 and Bowl 2. Bowl 1 contains 25% chocolate and 75% vanilla cookies; Bowl 2 has 50% of each. For this problem, assume each bowl is large enough that drawing a single cookie does not appreciably alter this ratio.

Suppose we draw two cookies from the bowl and they are both chocolate. Calculate the posterior probabilities of the two bowls in two ways:

(a) by treating the two cookies as one simultaneous piece of evidence

(b) by updating the prior probabilities once using the first chocolate cookie, and using the posterior probabilities as prior probabilities in a second update

Answer 1