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You begin the game Roll and Win by picking a number. Then you roll two regular dice, each numbered 1 through 6, and add the numbers that come up together. If the sum is the number you chose, you win a point. For example, if you choose “11,” and a 6 and a 5 are rolled, you win! What is P(even)? P(10)? P(15)? Which sum is the most likely result? What is the probability of rolling that sum? In a standard casino dice game the roller wins on the first roll if he rolls a sum of 7 or 11. What is the probability of winning on the first roll? The player loses on the 1st roll if he rolls a sum of 2, 3, or 12. What is the probability of losing on the 1st roll?If the player rolls any other sum, he continues to roll the dice until the first sum he rolled comes up again or until he rolls a sum of 7 or 11, whichever happens sooner. What is the probability that the game continues after the first roll?
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