16_R

Based on 15R, the few examples of relation between probability and relative frequency are presented in this post.

Coin toss [1]:

Probability example. You have a fair coin (with equal probability = 1/2). You toss it 100 times. What is the probability of 60 or more heads? We can get only a single answer because of the standard computation strategy.

Statistics example. You have a coin of unknown provenance. To investigate whether it is fair you toss it 100 times and count the number of heads. Let’s say you count 60 heads. Your job as a statistician is to draw a conclusion (inference) from this data. In this situation, different Statisticians may draw different conclusions because they may use different conclusion forms or may use different methods for predicting the probability(e.g. of landing heads)

The similar example is rolling a die [2].

Probability example. You have a fair die(with equal probability of outcomes: 1, 2, 3, 4, 5, and 6.). You roll it 100 times. What is the probability of rolling "6" 10 or more times ? This can be computed using formula/computation strategy. Based on that, we can expect it to roll approximately 16 times out of 100.

Statistics example. Here, you conduct an experiment to check whether it is true or not. You roll it 100 times. And based on the result you draw inference from collected data.

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References

1. https://towardsdatascience.com/probability-vs-statistics-95f221cc74f7

2. https://mathbitsnotebook.com/Geometry/Probability/PBTheoEmpirical.html