Question

a pair of standard dice are rolled. find the probability of rolling a sum of 10 with these dice. p(d₁ + d₂ = 10) = ? / be sure to reduce.

Explanation:

Step1: Calculate total number of outcomes

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

Step2: Find the number of favorable outcomes

The pairs \((D_1,D_2)\) that sum to 10 are \((4,6)\), \((5,5)\), \((6,4)\). So there are 3 favorable outcomes.

Step3: Calculate the probability

The probability \(P\) is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P=\frac{3}{36}\).

Step4: Simplify the fraction

Simplify \(\frac{3}{36}\) by dividing both the numerator and the denominator by 3. \(\frac{3\div3}{36\div3}=\frac{1}{12}\).

Answer:

\(\frac{1}{12}\)