To find the probability of picking either number 2 or number 3 from the sample space \( S = { 1, 2, 3 } \), we first note the probabilities of each individual outcome, which is \( \frac{1}{3} \).
The outcomes that satisfy the condition of picking either 2 or 3 are:
- Number 2
- Number 3
The probability of picking number 2 is \( \frac{1}{3} \), and the probability of picking number 3 is also \( \frac{1}{3} \).
To find the combined probability of picking either number 2 or number 3, we add the probabilities of these two outcomes together:
\[ P(2 \text{ or } 3) = P(2) + P(3) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \]
Thus, the probability of picking number 2 or number 3 is \( \frac{2}{3} \).