The GATE Grind

GATE 2021 EE – Question 37

Engineering Mathematics · Probability and Statistics: Random variables · 2 marks · Multiple choice

Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

  1. $p/(1-p)$
  2. $(1-p)/p$
  3. $1/p$
  4. $1/p^2$

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Show answer and explanation

Correct answer: (C) $1/p$

Explanation

The number of tosses until the first head is geometric with success probability $p$, so its mean is $\frac1p$.