Question

If two unbiased dice are thrown at a time, then find the probability of getting the sum of the number on the dice is 10?

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{12} \)
• C. \( \frac{1}{9} \)
• D. \( \frac{1}{8} \)

Hint:

When calculating the probability of an event, make sure to count the favorable outcomes correctly. In this case, count all the pairs that add up to the desired sum.

Answer 1

The Correct Option is B

When two unbiased dice are thrown, the total number of possible outcomes is $6 \times 6 = 36$.
We want to find the probability that the sum of the numbers on the dice is 10.
Let's list the favorable outcomes, i.e., the pairs of numbers that add up to 10.
The possible pairs are:
- (4, 6) - (5, 5) - (6, 4)
There are 3 favorable outcomes.
The probability of an event is calculated using the formula:
$P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}$.
$P(\text{sum is 10}) = \frac{3}{36}$.
Simplify the fraction by dividing both the numerator and the denominator by 3.
$P(\text{sum is 10}) = \frac{1}{12}$.