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: Count the total number of outcomes

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

Step2: Count the number of favorable outcomes

The even numbers in the set \(\{1,2,3,4,5,6,7,8,9,10\}\) are \(2,4,6,8,10\). So the number of favorable outcomes \(n(E) = 5\).

Step3: Use the probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 5\) and \(n(S)=10\), we get \(P(E)=\frac{5}{10}\).

Step4: Simplify the fraction

Simplify \(\frac{5}{10}\) by dividing both the numerator and the denominator by their greatest common divisor (which is 5). So \(\frac{5\div5}{10\div5}=\frac{1}{2}\).

Answer:

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