Five Heads, Five Tails

[Puzzle Prime]

If you throw a fair coin 1000 times, what is the expected number of occurrences of 5 heads followed by 5 tails?

[Vivek]

990/2^10 ? I tried using indicator variables. But not sure of the answer. Is there any other way?

[Puzzle Prime]

Yeah, this is the simplest solution. Just use linearity of expectation to reduce to 990 times the probability of HHHHHTTTTT. Good job! 🙂