To find the long-run relative frequency of heads after tossing a coin 500 times, where tails was observed 200 times, we first need to determine the number of times heads was observed.
If tails was observed 200 times, then the number of times heads was observed can be calculated as follows:
\[ \text{Number of heads} = \text{Total tosses} - \text{Number of tails} = 500 - 200 = 300 \]
Now, to find the long-run relative frequency of heads, we divide the number of heads by the total number of tosses:
\[ \text{Relative frequency of heads} = \frac{\text{Number of heads}}{\text{Total tosses}} = \frac{300}{500} = 0.6 \]
Thus, the long-run relative frequency of heads in decimal form is 0.6.