Question

a 10 - sided die is rolled. find the probability of rolling an even number. the set of equally likely outcomes is shown below.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
the probability of rolling an even number on a 10 - sided die is
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine total outcomes

Total outcomes when rolling a 10 - sided die: \(n(S)=10\) (since the set is \(\{1,2,3,4,5,6,7,8,9,10\}\)).

Step2: Identify favorable outcomes

Even numbers in the set: \(2,4,6,8,10\). So, number of favorable outcomes \(n(E) = 5\).

Step3: Calculate probability

Probability formula: \(P(E)=\frac{n(E)}{n(S)}\). Substitute \(n(E) = 5\) and \(n(S)=10\), we get \(P(E)=\frac{5}{10}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)