You have two opponents with whom you alternate play. Whenever you play A, you win with probability pA; whenever you play B, you win with probability pB , where pB > pA. If your objective is to minimize the number of games you need to play in order to win two in a row, should you start with A or B?

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?