GATE_AE_2027_MOCK_02_Q08 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) MCQ · 2 Marks
General Aptitude • Quantitative Aptitude • Permutations, Combinations & Probability

An aerospace telemetry system transmits a 4-bit binary code. If each bit has an independent error probability of $p = 0.05$, what is the probability that a transmitted word contains exactly one bit error? (Round to three decimal places).

(A) 0.171
(B) 0.050
(C) 0.185
(D) 0.005
Answer Key:
A

Step-by-Step Verified Solution

### Solution: $P(X = 1) = \binom{4}{1} p^1 (1-p)^3 = 4 \times 0.05 \times (0.95)^3 = 0.20 \times 0.857375 = 0.171475 \approx 0.171$. Correct: A.
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