Probability
Independent Events
Grade 12
Question:
<p>Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is</p>
<p>(a) 0.06</p>
<p>(b) 0.14</p>
<p>(c) 0.32</p>
<p>(d) 0.7</p>
Step-by-Step Solution
Key Concept: The second plane only gets to bomb if the first misses. Use multiplication rule for independent events.
<p><strong>Solution:</strong></p><p>For the second plane to hit the target, the first plane must miss and the second must hit.</p><p>P(first misses) = 1 - 0.3 = 0.7</p><p>P(second hits) = 0.2</p><p>P(target hit by second plane) = P(first misses) × P(second hits)</p><p>\(= 0.7 \times 0.2 = 0.14\)</p>
Correct Answer: B