Q.35 Two fair six-sided dice, with sides numbered 1 to 6, are thrown once. The
probability of getting 7 as the sum of the numbers on the top side of the
dice is _____________.
(Round off to two decimal places)
six-sided dice is 0.17 when rounded to two decimal places.
This result comes from 6 favorable outcomes out of
36 total possible outcomes.
Correct Answer
0.17
Step-by-Step Probability Calculation
Each die has 6 faces, and the rolls are independent. Therefore, the total
number of possible outcomes is:
6 × 6 = 36
The favorable outcomes that give a sum of 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
There are exactly 6 such outcomes. Hence, the probability is:
Probability = 6 / 36 = 1 / 6 ≈ 0.1667
Rounded to two decimal places:
Probability = 0.17
Why the Sum of 7 Stands Out
When rolling two dice, possible sums range from 2 to 12.
The sum of 7 has the highest probability because it can be
formed in more ways than any other sum.
For comparison:
- Sum of 6 → 5 outcomes → 5/36 ≈ 0.14
- Sum of 8 → 5 outcomes → 5/36 ≈ 0.14
This makes 7 the most likely single-sum event in dice games such as
craps.
Common Misconceptions
- All sums are equally likely:
Incorrect. While sums range from 2 to 12, they are not equally probable. - Using unordered pairs:
Treating (1,6) and (6,1) as the same outcome reduces the total incorrectly
and gives a wrong probability. - Rounding too early:
Always keep the exact fraction 1/6 until the final step
to avoid rounding errors.
