Question 3.12

[luca]

Q 3.12) You throw a fair coin million times. What is the expected number of strings of 6H followed by 6T?

So, the solution says the answer is 1/2^12 * (1M - 11). If we were to change the question to, "if we throw a fair coin 6 times, what is the expected number of strings of HH?", would the answer be 1? Because we know that the expected number of tosses to get one string of HH is 6. I am not sure if one implies the other. But if it does, then application of the method in Q 3.12 does not give 1.

Applying the solution in this case, E[number of HH] = 1/2^2 * (6 - 1) = 5/4. Please correct me if my understanding is wrong here.

Thanks

[mj]

the two questions are different.

[harmonic]

mj, can you give some hints to the two related questions? thanks.

[mj]

http://www.markjoshi.com/books/phpBB3/viewtopic.php?f=17&t=254