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. What is the distribution of the number of members in Party II who will favor Prop 88 tomorrow?

30 members.

Step-by-step explanation:

Given that in a group of 100 politicians, 40 are in Party I and 60 are in Party II, and that the members of the latter Party change their minds completely randomly every day, independently of all others and also independently of all evidence, knowing that of the 60 members in Party II, 10 are in favor and 50 are against Proposition 88 and 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, to determine the distribution of the number of members in Party II who will favor Prop 88 the following logical reasoning must be performed:

In every coin toss there is a 50% chance that it will come up heads, and a 50% chance that it will come up dry. Thus, we could affirm that each member of Party II has a 50% chance of changing their vote, that is, that an estimated half of the members will change their position. Thus, knowing that initially 10 are in favor and 50 are against Proposition 88, in case half changes their position, the 10 in favor would become 5 in favor and 5 against, and the 50 against would become 25 for and 25 against. In this way, some 30 members of Party II will favor Prop 88.