The theoretical probability of a fair coin landing heads up is calculated based on the assumption that there are two equally likely outcomes: heads and tails.
The formula for calculating the theoretical probability \( P \) of an event is:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (heads) is 1, and the total number of outcomes (heads or tails) is 2.
So, the theoretical probability of landing heads up is:
\[ P(\text{heads}) = \frac{1}{2} = 0.5 \]
To express this as a percentage, you can multiply by 100:
\[ P(\text{heads}) = 0.5 \times 100 = 50% \]
Thus, the theoretical probability of the coin landing heads up is 50%.