Over several years of experience of teaching probability, it has been observed again and again that students find it very difficult to interpret probability correctly. I believe this is mainly due to the following reason.
In teaching process as well as in evaluation process, the ability to ‘compute probability’ is given more importance than the ability to ‘understand probability’. This is possibly because evaluating ‘the understanding of probability’ is more challenging. Students are also unfortunately more interested in marks than the knowledge.
Having said this, probability interpretation , however, has remained debatable for decades. Before I give my views on that here are some excerpts ..
‘Interpreting probability’ is a commonly used but misleading characterization of a worthy enterprise. The so-called ‘interpretations of probability’ would be better called ‘analyses of various concepts of probability’, and ‘interpreting probability’ is the task of providing such analyses. Or perhaps better still, ….
The word probability has been used in a variety of ways since it was first coined in relation to games of chance. Does probability measure the real, physical tendency of something to occur, or is it just a measure of how strongly one believes it will occur? …
The single term probability can be used in several distinct senses. These fall into two main groups. A probability can be a limiting ratio in a sequence of repeatable events. Thus …
– From the book: Interpreting probability: Controversies and developments in the early twentieth Century, by David Howie; Cambridge University Press
This section considers two important interpretations of probability. …. And very intelligent people still disagree. So don’t expect this to be resolved by the present discussion.
– J. Pitman in his book Probability published by Springer.
TO BE CONTINUED …