In a certain game a participant is allowed three attempts at scoring a hit. In the three attempts he must alternate which hand is used; thus he has two possible strategies: right hand, left hand, right hand; or left hand, right hand, left hand. His chance of scoring a hit with his right hand is .8, while it is only .5 with his left hand. If he is successful at the game provided that he scores at least two hits in a row, what strategy gives the better chance of success? Answer the same question if .8 is replaced by P1 and .5 by P2. Does your answer depend on P1 and P2?