Question

seven different names are written into sticks and placed into a cup. A stick is chosen 100 times,out of which the name Grace is chosen 23 times. How do the theoretical probability and experimental probability compare? Explain why there is a discrepancy between them, if there is any.

Answer 1

The experimental and theoretical probabilities are considerably different. This has to do with the small number of trials. For a higher number of trials, the experimental probability should be very close to the theoretical probability of 0.1429.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Theoretical probability:

The theoretical probability is calculated without considering previous trials.

Experimental probability:

Calculated considering previous trials.

For a small number of trials, these probabilities can differ, but the experimental probability approximates the theoretical as the number of trials increase.

Seven different names are written into sticks and placed into a cup.

So the theoretical probability of choosing Grace is:

`p_T = (1)/(7) = 0.1429`

A stick is chosen 100 times,out of which the name Grace is chosen 23 times.

So the experimental probability is:

`p_E = (23)/(100) = 0.23`

How do the theoretical probability and experimental probability compare?

The experimental and theoretical probabilities are considerably different. This has to do with the small number of trials. For a higher number of trials, the experimental probability should be very close to the theoretical probability of 0.1429.