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

Each die has 6 faces. When two dice are rolled, the total number of outcomes is \(6\times6 = 36\) (by the fundamental counting principle).

Step2: Find number of favorable outcomes

Let the outcomes of the first die be \(x\) and the second die be \(y\). We want \(x + y=11\) where \(1\leq x\leq6\) and \(1\leq y\leq6\).
The possible pairs \((x,y)\) are \((5,6)\) and \((6,5)\). So the number of favorable outcomes \(n = 2\).

Step3: Calculate the probability

The probability formula is \(P=\frac{n}{N}\), where \(n\) is the number of favorable outcomes and \(N\) is the total number of outcomes.
Substituting \(n = 2\) and \(N=36\), we get \(P=\frac{2}{36}=\frac{1}{18}\).

Answer:

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