Assorted candies II: You have 4 bags of mixed candies on the table. They are leftovers from a party, so naturally there are only Almond Joys (A) and Twizzlers (T) left. The contents are as follows:

a. A bit tired from tidying up, you zone out and pick a bag at random.
You start picking out candies, looking at them, then returning them to their bag. You repeat this 7 times, and observe ATTATAA.
i. What are the (prior) probabilities that you had picked the different bags?
ii. What is the probability of your observation, given the different bags.
iii. Now find the posterior probabilities for the bags.

b. You pick three more pieces and return them, this time getting LKL. Update the probabilities for the bags on the basis of this new information.

c. A bit later you put the bag back, and you are joined by your brother.
Like you, he picks a bag at random, and then he picks out a fewpieces.
But unlike to you, he eats them. He eats TTA. Find, for each of the bags, the updated probability that it was picked by your brother.

Transcribed Image Text:

bag 1:5 Almond Joys and 3 Twizzlers bag 2: 7 Almond Joys and 8 Twizzlers bag 3: 2 Almond Joys and 9 Twizzlers bag 4: 11 Almond Joys and 13 Twizzlers.