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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

Question

Dua buah dadu diundi satu kali sekaligus. Peluang muncul kedua mata dadu berjumlah 10 atau kedua mata dadu sama adalah …….

:a. 1/36
:b. 5/36
:c. 7/36
:d. 3/36
:e. 8/36

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Solution

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: 6×6=36 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 (for sum 10)+6 (for same)1 (overlap)=8 unique outcomes 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(sum of 10 or same)=Number of favorable outcomesTotal outcomes=836=29 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 836 \frac{8}{36} or simplified, 29 \frac{2}{9} , which corresponds to option e.

This problem has been solved

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