Final answer:
The question requires finding the correlation between H100 and H300, which is the number of heads in the first 100 tosses and the total heads in 300 tosses of a fair coin, respectively. The correlation is sqrt(1/3) since H100 is a subset of H300.
Step-by-step explanation:
The question asks to find the correlation between H100, the number of heads in the first 100 tosses, and H300, the total number of heads after 300 tosses of a fair coin. The correlation, in this case, measures the degree to which the two variables are linearly related.
Firstly, since a fair coin is involved, each toss is independent of the others, and we would expect a 50% chance of getting a head on any given toss.
H100 is a part of H300, because the first 100 tosses are included in the 300 tosses. Therefore, there is a positive correlation because H100 contributes to the total H300.
Specifically, H100 is directly included in H300, so their correlation is the ratio of the standard deviations of H100 and H300 multiplied by the square root of the number of tosses from H100 (100) over total tosses (300), so the correlation is sqrt(100/300) or sqrt(1/3).