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NDA 1 2025 Maths, question 118

Topic: Probability

Q118

The probability of a man hitting a target is 1/5. If the man fires 7 times, then what is the probability that he hits the target at least twice?

  1. (a) 1−(3/5)(4/5)61 - (3/5)(4/5)^{6}
  2. (b) 1−(3/5)(4/5)71 - (3/5)(4/5)^{7}
  3. (c) 1−(11/5)(4/5)61 - (11/5)(4/5)^{6}Correct answer
  4. (d) 1−(11/5)(4/5)71 - (11/5)(4/5)^{7}

Solution.

Answer: (c) 1−(11/5)(4/5)61 - (11/5)(4/5)^{6}

  1. With independent shots of the same hit probability, the hit count is binomial.
  2. At least two hits is the complement of zero or one hit.
  3. Thus P(X≥2)=1−(4/5)7−7(1/5)(4/5)6=1−(11/5)(4/5)6P(X \geq 2) = 1 - (4/5)^{7} - 7(1/5)(4/5)^{6} = 1 - (11/5)(4/5)^{6}.