Question

a pair of standard dice are rolled. find the probability of rolling a sum of 12 with these dice. p(d₁ + d₂ = 12) = ? / be sure to reduce.

Explanation:

Step1: Determine the total number of outcomes

When rolling two standard dice, each die has 6 possible outcomes. By the fundamental counting principle, the total number of outcomes when rolling two dice is \(6\times6 = 36\).

Step2: Determine the number of favorable outcomes

The sum of two dice is 12. The only combination to get a sum of 12 is \((6,6)\), so there is 1 favorable outcome.

Step3: Calculate the probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P=\frac{1}{36}\).

Answer:

\(\frac{1}{36}\)