An employee buys a 50,000$ health insurance for 1,200$ good for one year. Based on his previous health records, the probability that this employee will be hospitalized in one year is 0.6541. Find tha payoff valur of the policy.

1. An employee buys a 50,000$ health insurance for 1,200$ good for one year. Based on his previous health records, the probability that this employee will be hospitalized in one year is 0.6541. Find tha payoff valur of the policy.

2. A player draws a card at random from a standard deck of 52 cards. If the card drawn is black, the player wins 2,000$ but if it is red, he loses the same amount. Find the expected value of the game.

3. A roulette wheel contains 30 numbers: 20 are blue and 10 are green. The roulette is fair which means that it is equally likely to land on any of the 30 numbers. You win 300$ if the roulette lands on a blue number; otherwise, you lose 200$. What is the expected value or payoff of the game.

4. A lottery that pays off 300,000,000$ is made available for 10,000,000 tickets. Each tickets costs 50$. Suppose the variable Z gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?