The Indiana University basketball team trails by 2 points with 8 seconds to go and has the ball. Should it attempt a 2-point shot or a 3-point shot? Assume that the Indiana shot will end the game and...

The Indiana University basketball team trails by 2 points with 8 seconds to go and has the ball. Should it attempt a 2-point shot or a 3-point shot? Assume that the Indiana shot will end the game and that no foul will occur on the shot. Assume that a 3-point shot has a 30% chance of succeeding, and a 2-point shot has a 45% chance of success. Finally, assume that Indiana has a 50% chance of winning in overtime.