Questions: An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is 8. What is the probability of getting a sum of 8 ? (Simplify your answer. Type a fraction.) Data table Second Die First Die 1 2 3 4 5 6 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is 8.

What is the probability of getting a sum of 8 ? (Simplify your answer. Type a fraction.)

Data table

 Second Die
 First Die  1  2  3  4  5  6
  1  (1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)
  2  (2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)
  3  (3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)
  4  (4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)
  5  (5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)
  6  (6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)
Transcript text: An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is 8. Click the icon to view the sample space. What is the probability of getting a sum of 8 ? (Simplify your answer. Type a fraction.) $\square$ Data table \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{8}{|c|}{Second Die} \\ \hline \multirow{7}{*}{First Die} & & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline & 1 & (1,1) & $(1,2)$ & $(1,3)$ & (1,4) & (1,5) & $(1,6)$ \\ \hline & 2 & $(2,1)$ & $(2,2)$ & $(2,3)$ & $(2,4)$ & $(2,5)$ & $(2,6)$ \\ \hline & 3 & $(3,1)$ & $(3,2)$ & $(3,3)$ & $(3,4)$ & $(3,5)$ & $(3,6)$ \\ \hline & 4 & $(4,1)$ & $(4,2)$ & (4,3) & (4,4) & (4,5) & $(4,6)$ \\ \hline & 5 & $(5,1)$ & $(5,2)$ & $(5,3)$ & $(5,4)$ & $(5,5)$ & $(5,6)$ \\ \hline & 6 & $(6,1)$ & $(6,2)$ & $(6,3)$ & $(6,4)$ & $(6,5)$ & $(6,6)$ \\ \hline \end{tabular} Print Done Get more help -
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Solution

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Solution Steps

To find the probability of getting a sum of 8 when rolling two dice, we first need to identify all possible outcomes that result in this sum. Then, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. The total number of possible outcomes when rolling two dice is 36 (6 sides on the first die multiplied by 6 sides on the second die).

Step 1: Total Outcomes

When rolling two fair dice, the total number of possible outcomes is calculated as follows: \[ \text{Total Outcomes} = 6 \times 6 = 36 \]

Step 2: Favorable Outcomes

Next, we identify the outcomes that result in a sum of 8. The pairs that yield this sum are: \[ (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) \] Thus, the number of favorable outcomes is: \[ \text{Favorable Outcomes} = 5 \]

Step 3: Probability Calculation

The probability \( P \) of rolling a sum of 8 is given by the ratio of favorable outcomes to total outcomes: \[ P(\text{sum} = 8) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{5}{36} \]

Final Answer

The probability of getting a sum of 8 when rolling two dice is \[ \boxed{\frac{5}{36}} \]

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