Question

mia is rolling a pair of 6 - sided dice.
$p(n)$ models the probability of the event that the sum of the dice is $n$.
which number type is more appropriate for the domain of $p$?
choose 1 answer:
integers
real numbers
whats the appropriate domain?
choose 1 answer:
$0\leq n\leq 12$
$0\leq n\leq 1$
$2\leq n\leq 12$
$\frac{1}{36}\leq n\leq \frac{6}{36}$

Explanation:

• For the number - type question:
• When rolling two 6 - sided dice, the sum \(n\) of the two dice (e.g., \(1 + 1=2\), \(1+2 = 3,\cdots,6 + 6=12\)) is always a whole number. Integers are whole numbers (positive, negative, or zero), while real numbers include fractions, decimals, and irrational numbers. Since the sum of two dice cannot be a non - whole number (e.g., you can't get a sum of \(2.5\) when rolling two standard dice), integers are the appropriate number type for the domain of \(P(n)\).
• For the domain question:
• The minimum value of the sum of two 6 - sided dice: The smallest number on a single die is \(1\). So, the minimum sum \(n_{\min}=1 + 1=2\).
• The maximum value of the sum of two 6 - sided dice: The largest number on a single die is \(6\). So, the maximum sum \(n_{\max}=6 + 6=12\).
• The values of \(n\) (the sum of the two dice) range from \(2\) to \(12\). The range \(0\leq n\leq12\) includes values (\(n = 0\) and \(n=1\)) that are not possible as sums of two 6 - sided dice. The range \(0\leq n\leq1\) represents probabilities (not the sum of dice). The range \(\frac{1}{36}\leq n\leq\frac{6}{36}\) also represents probabilities (not the sum of dice).

Answer:

A. Integers
C. \(2\leq n\leq12\)