Using the probability concept, it is found that:
- There is a 0.1545 = 15.45% experimental probability of the name Karen being chosen.
- There is a 0.125 = 12.5% theoretical probability of the name Karen being chosen.
- If the number of names in the hat was different, the total number of outcomes would for the theoretical probability would be different, hence with less names the probabilities would increase, with more names the probabilities would decrease.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the experimental probability, the numbers of outcomes are taken from previous trials, hence considering the name Karen was chosen 19 times out of 123, we have that:
[tex]p_E = \frac{19}{123} = 0.1545[/tex]
For the theoretical probability, the number of outcomes are taken from the "theory", that is, before the trials, hence considering that Karen is one out of 8 names:
[tex]p_T = \frac{1}{8} = 0.125[/tex]
If the number of names in the hat was different, the total number of outcomes would for the theoretical probability would be different, hence with less names the probabilities would increase, with more names the probabilities would decrease.
You can learn more about probabilities at https://brainly.com/question/15536019
