Suppose that a game of chance is played with a pair of fair10-sided dice (with the sides numbered 1 to 10). In the game, youcan pick any number from 1 to 10 and the two dice are then “rolledâ€in a cage. If $1 is bet and exactly one of the number that youpicked is rolled you win $1, and if both of the dice are the numberthat you picked you win $20 (in each of those cases you also getyour initial $1 bet back). If none of your number winds up beingrolled you lose your $1 bet. Suppose that you play this game 8times and pick the same number each time.
a) What is the probability that doubles of YOUR number (bothdice come up your number) does not occur in the 8 rolls?
b) What is your total expected win or loss? Indicate in youranswer both the amount (rounded to the nearest $0.01 if necessary)and whether it is a win or loss.
