Question

In a group of 100 politicians, 40 are in Party I and 60 are in Party II. Members of Party I are incapable of changing their minds about anything. Members of Party II change their minds completely randomly every day, independently of all others and also independently of all evidence.

Tomorrow, the politicians are going to vote on Proposition 88. Here is a summary of their opinions today.

• Of the 40 members in Party I, 25 are in favor of Prop 88 and 15 are against.
• Of the 60 members in Party II, 10 are in favor and 50 are against.

Assume that each member in Party II changes their mind based on the toss of a coin: if it lands heads they switch to the opposite opinion and if it lands tails they don't change their mind.

a) What is the distribution of the number of members in Party II who will favor Prop 88 tomorrow? In what way, if any, does it depend on the information given about the opinions of Party II members today?

b) Write a math expression for the chance that a majority (more than 50) of the 100 politicians favor Prop 88 tomorrow. Use the code cell below to compute it and provide the final numerical answer on paper along with your math expression.

Answer 1