<p>The probability that an automobile will be stolen and found within one week is 0.0006. The probability that an automobile will be stolen is 0.0015. The probability that a stolen automobile will be found in one week is</p>
Step-by-Step Solution
Key Concept: Use conditional probability formula: P(A|B) = P(A∩B)/P(B), where A is 'found within one week' and B is 'stolen'. The given joint probability and marginal probability directly yield the conditional probability.
<p><strong>Step 1:</strong> Identify given information.</p><p>Let S = automobile is stolen, F = automobile is found within one week</p><p>Given: P(S ∩ F) = 0.0006 and P(S) = 0.0015</p><p><strong>Step 2:</strong> Apply conditional probability formula.</p><p>We need to find P(F|S) = probability that a stolen automobile will be found in one week</p><p>Using: P(F|S) = P(S ∩ F) / P(S)</p><p><strong>Step 3:</strong> Calculate.</p><p>P(F|S) = 0.0006 / 0.0015 = 6/15 = 2/5 = 0.4</p><p>∴ Answer: B (0.4 or 2/5 or 40%)</p>
Correct Answer: B