Question

a pair of standard dice are rolled. find the probability of rolling a sum of 11 with these dice. p(d₁ + d₂ = 11) = ?

Explanation:

Step1: Calculate total number of outcomes

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

Step2: Find number of favorable outcomes

The pairs \((D_1,D_2)\) that sum to 11 are \((5,6)\) and \((6,5)\). So there are 2 favorable outcomes.

Step3: Calculate probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P=\frac{2}{36}=\frac{1}{18}\).

Answer:

\(\frac{1}{18}\)