Let's break down the two parts of your question regarding the probability of the coin landing heads up.
Part 1
The theoretical probability of a fair coin landing heads up is:
\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes (heads)}}{\text{Total possible outcomes}} = \frac{1}{2} = 0.5 \]
In percentage form, this is:
\[ 0.5 \times 100 = 50% \]
Answer for Part 1: 50%
Part 2
To find the experimental probability based on Liz's results, we use the number of times the coin landed heads up divided by the total number of flips:
\[ \text{Experimental Probability} = \frac{\text{Number of heads}}{\text{Total flips}} = \frac{48}{80} = 0.6 \]
In percentage form, this is:
\[ 0.6 \times 100 = 60% \]
Answer for Part 2: 60%
So, to summarize:
- The theoretical probability of the coin landing heads up is 50%.
- The experimental probability of the coin landing heads up based on Liz's results is 60%.