Answer the following conceptual questions about probability.

a) Suppose your friend Rudy says that the probability it rains tomorrow is 125 percent. Is Rudy’s statement coherent? Explain your answer.

b) Suppose Rudy assigns probability 0.3 to the sentence $(P\to Q)$.

What probability should Rudy assign to the sentence $(\sim P\vee Q)?$

Explain your answer.

c) Suppose Rudy buys a lottery ticket. You say, “Don’t you know how unlikely it is that you’ll win?” Rudy replies, “Either I’ll win or I won’t, so there’s a 50% chance!” Is Rudy correct?

What might you say to Rudy in this case?