A fair coin is flipped n times. Give an expression for each of the probabilities below as a function of n. Simplify your final expression as much as possible.

Insurance: An insurance company sells a 1-year term life insurance policy to an 79-year-old woman. The woman pays a premium of $1800. If she dies within 1 year, the company will pay $39,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 79-year-old woman will be alive 1 year later is 0.9561. Let X be the profit made by the insurance company. Part 1 of 2 (a) Find the probability distribution. The probability distribution is X -37200 1800 P(x) 0.0439 0.9561 Alternate Answer: X P(x) Part: 1 / 2 Part 2 of 2 - 37,200 1800 0.0439 0.9561 (b) Find the expected value of the profit. Expected value of the profit is S X 00

Insurance: An insurance company sells a 1-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $4000. If she dies within 1 year, the company will pay $53,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 80-year-old woman will be alive 1 year later is 0.9259. Let X be the profit made by the insurance company. Part: 0 / 2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is X P(x) 4000 ☑

Insurance: An insurance company sells a 1-year term life insurance policy to an 84-year-old woman. The woman pays a premium of $1400. If she dies within 1 year, the company will pay $46,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 84-year-old woman will be alive 1 year later is 0.9714. Let X be the profit made by the insurance company. Part: 0 / 2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is x 1400 X P(x)