probability Question

Question

Reference to this solution https://gateoverflow.in/3778/gate2005-it-32

Can any explain below line

Comments

which line?

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from starting

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see probability of head or tail=1/2 in any through of a coin

Now, if u have 1 throw it can be (H  or  T)- No success will be there

Now, 2nd toss will be (HH or TT)- 2 success will be there

for 3rd toss (THH or HTT) - 2 success will be there

So, every time getting 2 success

Now. put this thing in formula k.p(k)

got now