GATE 2023 EE – Question 45
The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is _____________ (Round off to 3 decimal places).
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Correct answer: 0.18 to 0.20
Explanation
The number of trials to the first head is geometric with mean $1/p=4$, so $p=\tfrac14$. The probability that the first head occurs on the second trial is $(1-p)p=\dfrac34\cdot\dfrac14=0.1875\approx0.188$.