Multiple choice

A coin is tossed until one observes a sequence of exactly three tails. The probability that the experiment comes to an end at $7 th$ toss is

  1. $\displaystyle \frac{7}{128}$
  2. $\displaystyle \frac{1}{128}$
  3. $\displaystyle \frac{1}{32}$
  4. $\displaystyle \frac{5}{128}$
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A Correct answer
AI explanation

For the experiment to end exactly at the 7th toss, the sequence must have no three consecutive tails in the first four tosses, and the last three tosses must be tails. The qualifying sequences for the first four tosses are HHTT, HTHT, HTTH, THHT, THTH, TTHH, and HHHT, yielding 7 valid sequences of length 7. Since each specific sequence of 7 tosses has a probability of (1/2)^7 = 1/128, the total probability is 7/128.

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