One application that uses all the probability theory that we have been studying lately is solved using probability trees. These problems involve conditional probability, so if you do not have not a good understanding of that section yet, you may want to revisit it before attempting to complete this assignment. Consider the following problem: Out of 100 US senators, 58 are Republicans and 42 are Democrats. Out of the 58 Republican senators, 37 are in favor of a recently proposed Bill. However, only 12 of the Democratic senators are in favor. We will use this information to fill out a probability tree and then a Venn diagram. Since 58/100 senators are Republican, this means that the probability a senator is republican is 0.58. Thus, 1 0.58 = 0.42 is the probability that a senator is a Democrat. Of the Republican senators, 37/58 = 0.64 is the probability a Republican senator votes for the Bill. Of the Democratic senators, 12/42 = 0.29 is the probability a Democratic senator is in favor of the Bill. ( ) = (|) x () The rule of thumb with a probability tree is as follows, any branch must add to 1. Recall