Question

Seven different names were put into a hat. A name chosen 100 times. And the name Michael is chosen 9 times. What is experimental probability of the name Michael being chosen? What is the theoretical probability of the name Michael being chosen? Use the pencil and paper. Explain how each probability would change if the number of names in the hat were different.

Answer 1

Experimental probability = 9 / 100

Theoretical probability = 1/7

Explanation:

The experimental probability of an event is written as :

P = number of times event occur / total number of trials

Experimental probability is based on the outcome of an experiment that has taken place.

Theoretical probability is based on expected outcome of an event.

P = number of expected or required outcomes / total possible outcomes

Experimental probability of choosing the name Michael is :

Number of times Michael is chosen / number of trials

Experimental probability = 9 / 100 = 0.09

Theoretical probability of choosing michael:

Number of names in hat = 7

Number of names called Michael in hat = required outcome = 1

P = 1 / 7

If the number of names in hat was different from 7, then the theoretical probability will change.

Also, if the number of times a name was chosen was different from 100, then number of trials will also change and hence, the experimental probability.