<p>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:</p><table border='1'><tr><th></th><th>Employed</th><th>Unemployed</th></tr><tr><td>Male</td><td>460</td><td>40</td></tr><tr><td>Female</td><td>140</td><td>260</td></tr></table><p>An employed person is selected at random. Find the probability that the chosen one is a male.</p>
Step-by-Step Solution
Key Concept: Conditional probability requires using only the subset of employed people as the sample space, not the entire population. The denominator must be the total number of employed persons, not all adults.
<p><strong>Step 1:</strong> Identify the condition: An employed person is selected at random. This restricts our sample space to only employed individuals.</p><p><strong>Step 2:</strong> Count employed males and total employed persons from the table.</p><p>Employed males = 460</p><p>Total employed = 460 (males) + 140 (females) = 600</p><p><strong>Step 3:</strong> Apply conditional probability formula.</p><p>P(male | employed) = (Number of employed males)/(Total number of employed) = 460/600</p><p><strong>Step 4:</strong> Simplify the fraction.</p><p>460/600 = 46/60 = 23/30</p><p>∴ Answer: <strong>23/30</strong></p>
Correct Answer: 23/30