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
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
-
Total Possible Outcomes: When rolling two dice, each die has 6 faces. Thus, the total outcomes are:
-
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.
-
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.
-
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:
4. Verify and Summarize
To find the probability:
Final Answer
The probability that the sum of the two dice is 10 or both dice show the same number is or simplified, , which corresponds to option e.
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