Question

a 10 - sided die is rolled. find the probability of rolling an odd 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 odd number on a 10 - sided die is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of odd numbers

The odd numbers in the set \(\{1,2,3,4,5,6,7,8,9,10\}\) are \(1,3,5,7,9\). So there are \(n = 5\) odd numbers.

Step2: Determine the total number of outcomes

The total number of outcomes when rolling a 10 - sided die is \(N=10\).

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{n}{N}\). Substituting \(n = 5\) and \(N = 10\), we get \(P=\frac{5}{10}\). Simplifying \(\frac{5}{10}\) by dividing both the numerator and the denominator by 5, we have \(P=\frac{1}{2}\).

Answer:

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