A certain number of dollars is placed in each of two envelopes. The amounts differ from one another, but you do not know what the values of the two amounts are. You do know that they lie between 2 positive integers s and b, where 0 < s < b (where b > s + 2). You choose an envelope randomly. After inspecting its contents, you may switch envelopes. What is the probability of winning the larger sum of money if you use the following procedure:
- Choose an envelope and look to see how much cash is inside.
- Pick a random integer between s and b.
- If the number you drew is greater than the amount of cash in your envelope, you exchange the envelope. Otherwise, you keep the envelope you have.