Question

Challenge  Six different names were put into a hat. A name is chosen 114 times and the name Michael is chosen 11 times. What is the experimental probability of the name Michael being​ chosen? What is the theoretical probability of the name Michael 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 Michael is
  
StartFraction 11 Over 114 EndFraction
.
​(Type an integer or a simplified​ fraction.)
Part 2
The theoretical probability of choosing the name Michael is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

Part 1: Experimental probability = 11/114.

Part 2: Theoretical probability = 1/6.

Explanation: The experimental probability is the observed frequency (11 out of 114) so it stays 11/114 unless you actually change the trials or outcomes. The theoretical probability assumes all 6 names are equally likely, so P(Michael) = 1/6. If the hat had n different names (all equally likely), the theoretical probability would be 1/n (so it decreases as n increases and increases as n decreases). If names are not equally likely (or some names are repeated), the theoretical probability would change accordingly.