A divide-and-conquer form of yes/no questioning is an efficient way to determine

Question

A divide-and-conquer form of yes/no questioning is an efficient way to determine which "half" of a data set the answer to a generic question lies. We consider this manner of questioning in the following problem. A) Given that there are 30 teams in Major League Baseball (MLB), at the maximum when using a divide-and-conquer form of questioning, how many yes/no questions should it require to determine Nate's favorite baseball team? Submit Answer Tries 0/12 B) Given that Nate's favorite team is in the National League Central division which consists of 5 of the 30 MLB teams, at the maximum when using a divide-and-conquer form of questioning, how many yes/no questions should it require to determine Nate's favorite baseball team? Submit Answer Tries o/12 C) Nate wears red when his team plays. Only two teams in the NLC of MLB wear predominately red uniforms (the Cardinals and the Reds). At the maximum when using a divide-and-conquer form of Questioning, how many yes/no questions should it require to determine Nate's favorite baseball team? Submit Answer Tries 0/12 D) What is the entropy of the information sought in parts A), B) and C)? A) bits of information B) bits of information C) bits of information Submit Answer Tries 0/12

Explanation / Answer

a) MLB has 30 teams divided in Three groups. So the first question to Nate can be:
is your favorite team in group AL. Suppose his answer is NO. so this tells us that his favorite team is in NL.

2nd question to him can be: Is your favorite team in NL East. suppose the answer is no again

3rd question to him can be: Is your favorite team in NL Central. suppose the answer is no again

So this makes his favorite team to be in NL West. and in this group we can ask him individually about different teams. suppose the answers to first four team is no. So this makes the last( or the fifth) team to be is favorite.

so maximum of 7 questions are required.

b) 4, as his answer to first questions can be no. so ultimately the 5th team would be his favorite.

c) Assuming that Nate wears red to support his team, we need to ask him about one team only. e.g. is The Reds your favorite team. If the answer is yes so The Reds is his favorite else The Cardinals is his favorite.

d) a 4.92

b 2.32

c 1

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