Dua buah dadu diundi satu kali sekaligus. Peluang muncul kedua mata dadu berjumlah 10 atau kedua mata dadu sama adalah …….:a.1/36b.5/36c.7/36d.3/36e.8/36

1. Break Down the Problem

We need to calculate the probability of getting a sum of 10 or both dice showing the same number when two dice are rolled.

2. Relevant Concepts

To do this, we'll first determine:

• The total possible outcomes when rolling two dice.
• The outcomes that give a sum of 10.
• The outcomes where both dice show the same number.

3. Analysis and Detail

1. Total Possible Outcomes: When rolling two dice, each die has 6 faces. Thus, the total outcomes are: $6 \times 6 = 36$

2. Outcomes that Give a Sum of 10: The possible combinations of dice rolls that result in a sum of 10 are:

   • (4, 6)
   • (5, 5)
   • (6, 4)

   This gives us 3 outcomes.

3. Outcomes where Both Dice are the Same: The possible combinations where both dice show the same number are:

   • (1, 1)
   • (2, 2)
   • (3, 3)
   • (4, 4)
   • (5, 5)
   • (6, 6)

   This gives us 6 outcomes.

4. Combined Outcomes: Both conditions can overlap; specifically, the combination (5, 5) for a sum of 10 is included in the same outcomes. Hence, we should count it only once:

   • Total unique outcomes for sum of 10 or both the same: $3 \text{ (for sum 10)} + 6 \text{ (for same)} - 1 \text{ (overlap)} = 8 \text{ unique outcomes}$

4. Verify and Summarize

To find the probability: $P(\text{sum of 10 or same}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{8}{36} = \frac{2}{9}$

Final Answer

The probability that the sum of the two dice is 10 or both dice show the same number is $\frac{8}{36}$ or simplified, $\frac{2}{9}$, which corresponds to option e.