GATE 2014 EC (EC3) – Question 38
Toss a fair coin until both head and tail have appeared at least once. Find the average number of tosses required.
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Show answer and explanation
Correct answer: 2.9 to 3.1
Explanation
The first toss always supplies one of the two outcomes. Subsequent independent tosses wait for the opposite outcome, with success probability1/2each time and mean waiting time2. Thus the total expected number is1+2=**3tosses**. The first toss must be included.