Question

Challenge  Seven different names were put into a hat. A name is chosen 115 times and the name Maya is chosen 19 times. What is the experimental probability of the name Maya being​ chosen? What is the theoretical probability of the name Maya being​ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
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Part 1
The experimental probability of choosing the name Maya is
  
StartFraction 19 Over 115 EndFraction
.
​(Type an integer or a simplified​ fraction.)
Part 2
The theoretical probability of choosing the name Maya is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

Part 1: Experimental probability = 19/115.

Part 2: Theoretical probability = 1/7.

Explanation: The experimental probability is based on the observed frequency (19 out of 115) so it stays 19/115 for this experiment regardless of how many names are in the hat. The theoretical probability assumes all names are equally likely; with 7 different names it is 1/7. If the number of names were changed to k distinct names, the theoretical probability would become 1/k (and repeated experiments would have an experimental probability that should approach 1/k as the number of trials grows).