Question

I can accept a ?$1200 bill or play a game ten times. For each roll of the single? die, I win $600 for rolling 1 or? 2; I win $400 for rolling? 3; and I lose ?$200 for rolling? 4, 5, or 6. Based on the expected? value, What is the expected value after ten rolls?

Answer 1

Since each roll is independent from the other rolls so the Expected value in one roll will also be independent of the other rolls, so basically we can just sum up expectations for all rolls to get the value for 10 rolls and since each roll is basically the same event with values for all numbers on the dice so the expected value for all the rolls will be same.

So we can calculate the expected value for one roll and multiply it by 10 to get the total value for 10 rolls .

Expected value for 1 roll E(1 Roll) = 2 * 1 / 6 * 600 + 1 / 6 * 400 - 3 * 1 / 6 * 200 which is basically numbers multiplied by the probability to get any number multiplied the value associated

Therefore E(1 Roll) = 1000/6

Therefore E(10 Rolls) = 10000/6