Probability
Independent Events
Grade 12
Question:
<p>Three ships \(A\), \(B\), and \(C\) sail from England to India. If the ratio of their arriving safely are 2:5, 3:7, and 6:11, respectively, then the probability of all the ships for arriving safely is</p>
<p>(1) 18/595</p>
<p>(2) 6/17</p>
<p>(3) 3/10</p>
<p>(4) 2/7</p>
Step-by-Step Solution
Key Concept: Convert ratio format (a:b means probability = a/(a+b)) to individual probabilities, then multiply independent events for 'all arrive safely' scenario.
<p><strong>Step 1:</strong> Convert each ratio to probability form.</p><p>For ship A with ratio 2:5 → P(A arrives safely) = 2/(2+5) = 2/7</p><p>For ship B with ratio 3:7 → P(B arrives safely) = 3/(3+7) = 3/10</p><p>For ship C with ratio 6:11 → P(C arrives safely) = 6/(6+11) = 6/17</p><p><strong>Step 2:</strong> Since the ships sail independently, use multiplication rule for independent events.</p><p>P(all three arrive safely) = P(A) × P(B) × P(C)</p><p>= (2/7) × (3/10) × (6/17)</p><p>= (2 × 3 × 6)/(7 × 10 × 17)</p><p>= 36/1190</p><p>= 18/595</p><p>∴ Answer: A (or 18/595 depending on options provided)</p>
Correct Answer: A