Question

Liz flips a coin 80 times. The coin lands heads up 48 times and tails up 32 times. Complete each statement.
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Part 1
The theoretical probability of the coin landing heads up is
  
enter your response here​%.
​(Type an integer or a​ decimal.)

Answer 1

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%**.