<p>If the probability for \(A\) to fail in an examination is 0.2 and that for \(B\) is 0.3 then the probability that either \(A\) or \(B\) fails is 0.5.</p>
Step-by-Step Solution
Key Concept: Use the complement principle: P(A or B fails) = 1 - P(both pass). Since failures are independent events, multiply individual passing probabilities: P(both pass) = P(A passes) × P(B passes) = (0.8)(0.7) = 0.56.
<p><strong>Step 1:</strong> Identify given information.</p><p>P(A fails) = 0.2 → P(A passes) = 0.8</p><p>P(B fails) = 0.3 → P(B passes) = 0.7</p><p><strong>Step 2:</strong> Find probability that either A or B fails using complement.</p><p>P(A or B fails) = 1 - P(both pass)</p><p>P(both pass) = P(A passes) × P(B passes) = 0.8 × 0.7 = 0.56</p><p><strong>Step 3:</strong> Calculate the required probability.</p><p>P(A or B fails) = 1 - 0.56 = 0.44</p><p><strong>Alternatively:</strong> Using addition formula:</p><p>P(A or B fails) = P(A fails) + P(B fails) - P(both fail)</p><p>= 0.2 + 0.3 - (0.2 × 0.3) = 0.5 - 0.06 = 0.44</p><p>∴ The statement is <strong>FALSE</strong>. The correct probability is 0.44, not 0.5. Answer: <strong>B</strong></p>
Correct Answer: B