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$A single die is rolled twice. The 36 equally-likely outcomes afre shown to the right. Find the probability of getting two numbers whose sum is 8 . The probability of getting two numbers whose sum is 8 is (1)/(8). (Type an integer or a simplified fraction.)$

A single die is rolled twice. The $36$ equally-likely outcomes afre shown to the right. $\newline$ Find the probability of getting two numbers whose sum is $8$ . $\newline$ The probability of getting two numbers whose sum is $8$ is $\frac{1}{8}$ . $\newline$ (Type an integer or a simplified fraction.)

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Probability of simple events

Full solution

Q. A single die is rolled twice. The

36

equally-likely outcomes afre shown to the right.

\newline

Find the probability of getting two numbers whose sum is

8

.

\newline

The probability of getting two numbers whose sum is

8

is

\frac{1}{8}

.

\newline

(Type an integer or a simplified fraction.)

Identify possible outcomes: First, we need to identify all the possible outcomes when rolling two dice that result in a sum of $8$ . The pairs are $(2,6)$ , $(3,5)$ , $(4,4)$ , $(5,3)$ , and $(6,2)$ . Each pair represents a unique outcome.
Count pairs for sum: Next, we count the number of pairs that sum up to $8$ . There are $5$ pairs as identified in the previous step.
Determine total outcomes: Now, we need to determine the total number of possible outcomes when rolling two dice. Since each die has $6$ faces, and each face can land in combination with any face of the other die, there are $6 \times 6 = 36$ possible outcomes.
Calculate probability: To find the probability of getting a sum of $8$ , we divide the number of favorable outcomes (sum equals $8$ ) by the total number of possible outcomes. So, the probability $P$ is $P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{36}$ .

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