Question

a single die is rolled twice. the 36 equally - likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 11. the probability of getting two numbers whose sum is 11 is. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the total number of outcomes

The total number of equally - likely outcomes when a die is rolled twice is \(n(S)=36\) (as given in the problem).

Step2: Find the number of favorable outcomes

Let the first roll result be \(x\) and the second roll result be \(y\). We want \(x + y=11\).
If \(x = 5,y = 6\) (i.e., the outcome \((5,6)\)) and if \(x = 6,y = 5\) (i.e., the outcome \((6,5)\)). So the number of favorable outcomes \(n(E)=2\).

Step3: Calculate the probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\).
Substitute \(n(E) = 2\) and \(n(S)=36\) into the formula: \(P(E)=\frac{2}{36}\).
Simplify the fraction \(\frac{2}{36}=\frac{1}{18}\) (divide both the numerator and the denominator by 2).

Answer:

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