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)________?
Somewhere it explain as:
$$1/4 + 1/4*1/4 + 1/4*1/4*1/4 + …..$$ Approx $0.33$
Can you explain in formal way, please?