2. Weather forecaster Gonnarain is so certain it will rain on Sunday that he would offer a bet of 3:2 that it will happen. Remember, if it rains after someone bets with Gonnarain, Gonnarain keeps all of the money. If it does not rain, then Gonnarain pays the better $3 for each $2 that was wagered. On a different channel, Alwaysunny is confident that on Sunday it will not rain; she offers 4:3 odds. (a) A person has $100. Set up a hedge where the person will win the same amount of money no matter what happens on Sunday. (b) Draw the two profit lines. (c) How much money is the person guaranteed to win no matter what happens? (d) Both forecasters believe they are making a fair bet; that is, they are willing to take either side. Determine the likelihood each has for rain on Sunday, for no rain on Sunday. (e) Add the probabilities of rain from Alwaysunny and of no rain from Gonnarain. Add the probabilities of rain from Gonnarain and no rain from Alwaysunny. What do you notice? How does the answer help you understand when a bet is to your advantage? 2. Weather forecaster Gonnarain is so certain it will rain on Sunday that he would offer a bet of 3:2 that it will happen. Remember, if it rains after someone bets with Gonnarain, Gonnarain keeps all of the money. If it does not rain, then Gonnarain pays the better $3 for each $2 that was wagered. On a different channel, Alwaysunny is confident that on Sunday it will not rain; she offers 4:3 odds. (a) A person has $100. Set up a hedge where the person will win the same amount of money no matter what happens on Sunday. (b) Draw the two profit lines. (c) How much money is the person guaranteed to win no matter what happens? (d) Both forecasters believe they are making a fair bet; that is, they are willing to take either side. Determine the likelihood each has for rain on Sunday, for no rain on Sunday. (e) Add the probabilities of rain from Alwaysunny and of no rain from Gonnarain. Add the probabilities of rain from Gonnarain and no rain from Alwaysunny. What do you notice? How does the answer help you understand when a bet is to your advantage