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

Step 1: Total outcomes.
When two unbiased dice are thrown, the total number of possible outcomes is the product of the number of faces on each die, which is: \[ 6 \times 6 = 36 \] So, there are 36 possible outcomes.

Step 2: Favorable outcomes.
We need to find the favorable outcomes where the sum of the numbers on the two dice is 10. The possible pairs of numbers that sum to 10 are: \[ (4, 6), (5, 5), (6, 4) \] Thus, there are 3 favorable outcomes.

Step 3: Probability.
The probability of an event is given by: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{36} = \frac{1}{12} \]

Final Answer: \( \frac{1}{12} \).