Members of a legislature often must vote repeatedly on the same bill. As time goes on, members may change their votes. Suppose that p₀ is the probability that an individual legislator favors an issue before the first roll call vote, and suppose that p is the probability of a change in position from one vote to the next. Then the probability that the legislator will vote “yes” on the nth roll call is given by

For example, the chance of a “yes” on the third roll call vote is

Suppose that there is a chance of p₀ = 0.7 that Congressman Stephens will favor the budget appropriation bill before the first roll call, but only a probability of p = 0.2 that he will change his mind on the subsequent vote. Find and interpret the following.
(a) p₂ 

(b) p₄
(c) p₈

(d)

Transcribed Image Text:

Pn 1 = 1₂ + (P₁ - 12) (₁ (1 - Po 2 - 2p)".