1. **State the problem:** We have a set $S = \{1,2,3,4,5,6,7,8,9,10\}$ and we want to find the probability that a number selected at random from $S$ is odd. 2. **Formula for probability:** The probability of an event $E$ is given by $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Identify favorable outcomes:** The favorable outcomes are the odd numbers in $S$. The odd numbers are $1, 3, 5, 7, 9$. 4. **Count favorable and total outcomes:** - Number of favorable outcomes = 5 - Total number of outcomes = 10 5. **Calculate the probability:** $$P(\text{odd number}) = \frac{5}{10} = \frac{1}{2}$$ 6. **Interpretation:** The probability that a randomly selected number from $S$ is odd is $\frac{1}{2}$ or 0.5.