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Question

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 outcoms are (TAILS, TAILS), then go to Step 1..

The probability that the output of the experiment is Y is 1k. Then k is

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Solution


From the tree diagram,
P(output=Y)=0.5×0.5+0.5×0.5×0.5×0.5+
It's an infinite G.P. with
a=0.5×0.5
r=0.5×0.5
P(output=Y)=0.2510.25=13
Hence k=3

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