You believe that next year there is 50% probability that your health care cost will be $5,000 but your spouse believes you will all be healthy and there will be no healthcare cost; however you both agree to buy an annual health insurance plan. An internet site makes you believe in your age group and with family size will spend $4,000 with 30% probability. You decide to make a scientific decision and look for a health insurance policy where the annual premium will not exceed your expected premium. What is your expected annual premium?