Consider a sample space `"S"` representing the adults in a small town who have completed the requirements for a college degree. They have been categorized according to sex and employment as follows: , Employed, Unemployed Male, 460, 40 Female, 140, 260 An employed person is selected at random. Find the probability that the chosen one is a male.

Explanation

To solve the problem step by step, we will calculate the probability that a randomly selected employed person is male.

### Step 1: Identify the total number of employed individuals.
From the data provided:
- Employed males = 460
- Employed females = 140

To find the total number of employed individuals, we add the number of employed males and employed females:
\[ \text{Total Employed} = \text{Employed Males} + \text{Employed Females} = 460 + 140 = 600 \]

### Step 2: Identify the number of employed males.
From the data, we know that the number of employed males is:
\[ \text{Employed Males} = 460 \]

### Step 3: Calculate the probability that the chosen employed person is male.
The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the event is selecting a male given that the person is employed. Thus, we can express this as:
\[ P(\text{Male | Employed}) = \frac{\text{Number of Employed Males}}{\text{Total Employed}} = \frac{460}{600} \]

### Step 4: Simplify the fraction.
We can simplify \(\frac{460}{600}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
\[ P(\text{Male | Employed}) = \frac{460 \div 20}{600 \div 20} = \frac{23}{30} \]

### Conclusion:
The probability that a randomly selected employed person is male is:
\[ \boxed{\frac{23}{30}} \]