The GATE Grind

GATE 2025 PI – Question 17

Quality and Reliability · Reliability and Maintenance · 1 mark · Multiple choice

An aircraft has two engines, each of reliability R. It crashes only if both stop. Find reliability against a crash.

  1. $R^2$
  2. $2R$
  3. $2R-R^2$
  4. $R^2-2R$

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Correct answer: (C) $2R-R^2$

Explanation

Assuming independent engine failures, both fail with probability $(1-R)^2$. Aircraft survival probability is $1-(1-R)^2=2R-R^2$: **C**. Independence is implicit; individual reliabilities alone do not determine joint failure probability.

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