Poker Dice is a poker-like game that you can play with a special set of dice; thesides are marked 9, 10, J, Q, K, A, like the high cards in a deck, but without suits.Each player rolls 5 dice, and attempts to form a poker hand (unlike poker, thisgame allow

(a) The probability of rolling four of a kind with five dice can be calculated as follows: - There are six possible values for the dice to show (9, 10, J, Q, K, A). - Choose one of these values to be the value that appears four times. This can be done in 6 ways. - For the dice that show the chosen value, there are five choices (the five dice). - For the remaining die, there are five choices (any of the six possible values except the chosen one). - Therefore, the total number of ways to roll four of a kind is 6 x 5 x 5 = 150. - The total number of possible rolls of five dice is 6^5 = 7,776. - Therefore, the probability of rolling four of a kind on the initial roll is 150/7,776, or \approx imately 1.93%. (b) The probability of rolling a full house with five dice can be calculated as follows: - Choose one of the six possible values to be the value that appears three times. This can be done in 6 ways. - For the dice that show the chosen value, there are five choices (the five dice). - Choose another value to be the value that appears twice (it cannot be the same as the first chosen value). This can be done in 5 ways. - For the dice that show the second chosen value, there are four choices (you only need two of the five dice). - Therefore, the total number of ways to roll a full house is 6 x 5 x 4 = 120. - The total number of possible rolls of five dice is 6^5 = 7,776. - Therefore, the probability of rolling a full house on the initial roll is 120/7,776, or \approx imately 1.54%.