Game Theory and Strategy Quiz 2: 1 December 2024 (September 2024 term)

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 1 red ball or 4 red balls and 1 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data answer the given subquestions.

Suppose one ball is picked from the blue majority urn. What is the probability that the ball is blue?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 1 red ball or 4 red balls and 1 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data answer the given subquestions.

What is the probability that the urn is blue-majority if the first student draws a red ball?

Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 1 red ball or 4 red balls and 1 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data answer the given subquestions.

Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red).
What is the probability of getting this sequence if the urn is a blue-majority urn?