Question

# Bunco is a group dice game that requires no skill. The objective of the game is...

Bunco is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations. The game is played with three dice, but we will consider a simpler version involving only two dice. How do you play two dice Bunco? There are six rounds, one for each of the possible outcomes in a die, namely the numbers one through six. Going clockwise, players take turns rolling two dice trying to score points. Points are usually awarded as such: 21 points if both dice match the current round number (a "Bunco"); five points are awarded if both dice match each other, but do not match the current round number (a "Mini Bunco"). Finally, one point is awarded for a single die matching the current round number. If points are scored, the player gets to roll again, continuing to add to their score. If no points are awarded, the player's turn ends and the dice are passed to the next player. At the end of the game, the winners get prizes for accomplishments such as the highest score, the lowest score, or the most buncos.

Part I: Complete the following steps assuming the round number is 6: What is the probability that the player rolls two distinct numbers different than six or rolls exactly one six (no points or one point)? What is the probability that the player rolls two of the same number but no six, i.e., two 1s, or two 2s, and so on (five points Mini Bunco)? What is the probability that the player rolls two 6s (21 points Bunco)? Compute the total of the probabilities found in the three previous questions. If the player wins a dollar for every point, he/she gets and losses three dollars for getting no points, what are the expected winnings or losses on each roll?