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A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of 3 ?
A.
(1)/(18)
B.
(1)/(4)
c.
(1)/(3)
D.
(4)/(9)
E.
(2)/(3)

Select the correct answer. $\newline$ A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of $3$ ? $\newline$ A. $\frac{1}{18}$ $\newline$ B. $\frac{1}{4}$ $\newline$ c. $\frac{1}{3}$ $\newline$ D. $\frac{4}{9}$ $\newline$ E. $\frac{2}{3}$

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Theoretical probability

Full solution

Q. Select the correct answer.

\newline

A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of

3

?

\newline

A.

\frac{1}{18}

\newline

B.

\frac{1}{4}

\newline

c.

\frac{1}{3}

\newline

D.

\frac{4}{9}

\newline

E.

\frac{2}{3}

Calculate Total Outcomes: First, let's determine the total number of possible outcomes when rolling two dice, one with $6$ sides and one with $8$ sides. The total number of outcomes is the product of the number of sides on each die. $\newline$ Total outcomes = $6$ (from the six-sided die) $\times$ $8$ (from the eight-sided die) = $48$ .
Find Favorable Outcomes: Next, we need to find the number of favorable outcomes, which are the pairs of numbers that add up to a multiple of $3$ . We can list these pairs or use a systematic approach to count them.
List Pairs Summing to $3$ : Let's list the pairs that sum to a multiple of $3$ : $(1,2)$ , $(1,5)$ , $(1,8)$ , $(2,1)$ , $(2,4)$ , $(2,7)$ , $(3,3)$ , $(3,6)$ , $(4,2)$ , $(1,2)$ $0$ , $(1,2)$ $1$ , $(1,2)$ $2$ , $(1,2)$ $3$ , $(1,2)$ $4$ , $(1,2)$ $5$ , $(1,2)$ $6$ .
Count Favorable Outcomes: Counting the pairs listed, we have a total of $16$ favorable outcomes.
Calculate Probability: Now, we can calculate the probability of getting a sum that is a multiple of $3$ by dividing the number of favorable outcomes by the total number of possible outcomes. $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{16}{48}$ .
Simplify Fraction: Simplify the fraction $\frac{16}{48}$ to its lowest terms. $\newline$ $\frac{16}{48}$ can be simplified by dividing both the numerator and the denominator by $16$ . $\newline$ $\frac{16}{48} = \frac{1}{3}$ .

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