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Probability question

2007 · Shift 0 · Q45
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  5. /2007 · Shift 0 · Q45

Probability question

2007 · Shift 0 · Q45

JEE MainMathematicsProbabilityMCQ+4 / −1
Two aeroplanes I{\rm I}I and II{\rm I}{\rm I}II bomb a target in succession. The probabilities of I{\rm I}I and II{\rm I}{\rm I}II scoring a hit correctly are 0.30.30.3 and 0.2,0.2,0.2, 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 :
  1. A
    0.20.20.2
  2. B
    0.70.70.7
  3. C
    0.060.060.06
  4. D
    0.32
View written solutionFree

Correct answer: 0.14

  1. Let:

    • P(I hits)=0.3P(\text{I hits}) = 0.3P(I hits)=0.3
    • P(II hits)=0.2P(\text{II hits}) = 0.2P(II hits)=0.2
  2. The second plane bombs only if the first plane misses.

    So first compute the probability that plane I misses: P(I misses)=1−0.3=0.7P(\text{I misses}) = 1 - 0.3 = 0.7P(I misses)=1−0.3=0.7

  3. For the target to be hit by the second plane, two things must happen:

    • plane I misses, and
    • plane II hits.

    Therefore, P(target hit by II)=P(I misses)⋅P(II hits)P(\text{target hit by II}) = P(\text{I misses}) \cdot P(\text{II hits})P(target hit by II)=P(I misses)⋅P(II hits)

  4. Substitute the values: P(target hit by II)=0.7×0.2=0.14P(\text{target hit by II}) = 0.7 \times 0.2 = 0.14P(target hit by II)=0.7×0.2=0.14

  5. So the required probability is: 0.14\boxed{0.14}0.14​

  6. Checking options:

    • A: 0.20.20.2 ❌
    • B: 0.70.70.7 ❌
    • C: 0.060.060.06 ❌
    • D: 0.320.320.32 ❌

    Hence, none of the given options matches the correct value.

  7. Comparison with stored correct answer:

    • Stored correct answer: D (0.320.320.32)
    • Derived answer: 0.140.140.14

    Therefore, the stored answer appears to be incorrect.

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