Question

Challenge  Six different names were put into a hat. A name is chosen 109 times and the name Ted is chosen 18 times. What is the experimental probability of the name Ted being​ chosen? What is the theoretical probability of the name Ted being​ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Question content area bottom
Part 1
The experimental probability of choosing the name Ted is
  
StartFraction 18 Over 109 EndFraction
.
​(Type an integer or a simplified​ fraction.)
Part 2
The theoretical probability of choosing the name Ted is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

Part 1
Experimental probability = 18/109.

Part 2
Theoretical probability = 1/6.

Explanation: The experimental probability is the observed frequency (18) divided by the number of trials (109). The theoretical probability, with six different names equally likely, is 1/6. If the number of names in the hat were changed to n, the theoretical probability would become 1/n. The experimental probability would be the observed number of times Ted is chosen divided by the total trials; with many trials it should approach the theoretical value 1/n.