If you are willing to pay $$\$ 1,000$$ for a used stereo that is a "cherry" and $$\$200 $$ for a used stereo that is a "lemon," how much will you be willing to offer to purchase a stereo if there is a 50 percent chance that the stereo is a lemon? If owners of cherry stereos want $$\$ 700$$ for their cherries, how will your estimate of the chance of getting a cherry change?