Question

Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being​ chosen? What is the theoretical probability of the name Grace being​ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.

Answer 1

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Explanation:

Experimental Probability:

The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:

Experimental Probability = Number of times Grace was chosen / Total number of trials

Experimental Probability = 15 / 116

Experimental Probability = 0.1293 or approximately 12.93%

Theoretical Probability:

The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:

Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes

Theoretical Probability = 1 / 6

Theoretical Probability = 0.1667 or approximately 16.67%

If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.