Questions: You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 10 -sided die and one 12 -sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, which of the following values are included in the random variable? 22 All of the above 23 1 16 0 20

You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 10 -sided die and one 12 -sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, which of the following values are included in the random variable?
22
All of the above
23
1
16
0
20

Transcript text: You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 10 -sided die and one 12 -sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, which of the following values are included in the random variable? 22 All of the above 23 1 16 0 20

Solution

Solution Steps

Step 1: Determine the Range of Possible Sums

When rolling a 10-sided die and a 12-sided die, the minimum sum occurs when both dice show their lowest value: \[ \text{min\_sum} = 1 + 1 = 2 \] The maximum sum occurs when both dice show their highest value: \[ \text{max\_sum} = 10 + 12 = 22 \] Thus, the range of possible sums is from \(2\) to \(22\).

Step 2: Identify Possible Sums

The possible sums when rolling the two dice are all integers from \(2\) to \(22\), inclusive: \[ \text{possible\_sums} = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22\} \]

Step 3: Check Included Values

We need to check which of the following values are included in the set of possible sums: