Question

When two dice are thrown, the probability of getting the sum of the values on them as 10 or 11 is:

• A. \( \frac{7}{36} \)
• B. \( \frac{5}{36} \)
• C. \( \frac{5}{18} \)
• D. \( \frac{7}{18} \)

Hint:

When dealing with dice probability, first list all the possible outcomes for the sum and then calculate the favorable outcomes.

Answer 1

The Correct Option is B

To find the probability of getting a sum of 10 or 11 when two dice are thrown, we proceed as follows: Step 1: Total number of outcomes When two dice are thrown, each die has 6 possible outcomes. Thus, the total number of outcomes is: \[ 6 \times 6 = 36. \] Step 2: Count favorable outcomes for sum = 10 The combinations of values on the two dice that result in a sum of 10 are: \[ (4, 6), \quad (5, 5), \quad (6, 4). \] Thus, there are 3 favorable outcomes for a sum of 10. Step 3: Count favorable outcomes for sum = 11 The combinations of values on the two dice that result in a sum of 11 are: \[ (5, 6), \quad (6, 5). \] Thus, there are 2 favorable outcomes for a sum of 11. Step 4: Total favorable outcomes The total number of favorable outcomes for a sum of 10 or 11 is: \[ 3 + 2 = 5. \] Step 5: Compute the probability The probability \( P \) of getting a sum of 10 or 11 is: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{36}. \] Final Answer: \[ \boxed{\frac{5}{36}} \]