GATE 2016 CS – Question 39
Consider the following experiment.
Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places) ________.
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Show answer and explanation
Correct answer: 0.33 to 0.34
Explanation
Each pair of flips has probability $\frac{1}{4}$. The experiment outputs Y right away with probability $\frac{1}{4}$, restarts with probability $\frac{1}{4}$ (for two tails), and outputs N otherwise. So $P = \frac{1}{4} + \frac{1}{4}P$, which gives $P = \frac{1/4}{3/4} = \frac{1}{3} \approx 0.33$.