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
- (A)
- (B)✓ Correct
- (C)
- (D)
Answer: (B)
Solution
The second plane bombs only if the first misses, so the target is hit by the second plane exactly when plane I misses and plane II hits: P = P(I misses)·P(II hits) = (1 − 0.3)(0.2) = 0.7 × 0.2 = 0.14 → option B. The stem describes a single succession (I, then II only if I missed), so this direct product is the required probability. The source left the key blank after summing an infinite alternating-rounds series to 7/22, but that re-interpretation does not match the single-succession wording.
JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option