A player throws a die whose faces are numbered 1 to 6 inclusive. If the player obtains a six he throws the die a second time, and in this case his score is the sum of 6 and the second number; otherwise his score is the number obtained. The player has no more than two throws. Let X be the random variable denoting the player's score. Write down the probability distribution of X, and determine the mean of X. Show that the probability that the sum of two successive scores is 8 or more is Determine the probability that the first of two successive scores is 7 or more, given that their sum is 8 or more. (C)