An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?

The probability that a 22-year-old female in the U.S. will die within one year is approximately 0.00044. If an insurance company sells a one-year, $20,000 life insurance policy to such a person for $295, what is the company's expectation? (Round your answer to the nearest dollar.)$

Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.3. If it rains, it will be sunny the next day with probability 0.4. Answer the following questions: 1. What is the probability that it will rain the next day if it was sunny the previous day? 2. Suppose that the weatherman estimates there is a 90% chance of showers today. Find the probability vector representing this estimation where the state 1 is sunny and state 2 is rainy. 3. Based on the meteorologistť's estimation, what is the chance of rain tomorrow? 4. Based on the meteorologist's estimation, What is the chance of rain two days from now?

An insurance policy on an electrical device pays a benefit of $2400 if the device fails during the first year. The amount of the benefit decreases by $800 each successive year until it reaches 0 . If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.29.Find the expected benefit under this policy.

A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.15. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the companys assumptions, calculate the probability that there are fewer than 3 tornadoes in a 15-year period. Round your answer to 4 decimals. Show your work. Show what you entered into your calculator.

In the game of roulette, a player can place a $6 bet on the number 11 and have a ag probability of winning. If the metal ball lands on 11, the player gets to keep the $6 paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $ (Round to the nearest cent as needed.)