What is the theoretical probability of choosing a winning four-digit number in the lottery

Question

what is theoretical probability and how do you find it? How do you find theoretical probability without a spinner.

Answer 1

PLZ be clear on the definitions:

  Theoretical probability = the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes.

  Experimental probability = the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

 

The difference is described by the words "is performed."  For example, the theoretical probability of a "fair" coin flip producing heads is 1/2 or 50% on each flip.  In fact, we may flip that coin all day and not get a heads (very low theoretical probability however).

 

For a single "winning" number to occur out of 10*10*10*10 possibilities (four digits of 0-9 with equal probability of occurring, that is, "fair"), we have 1/10,000.

 

However, it is easy to keep records of winning lottery numbers and see that they don't exactly occur in a uniform distribution (like theoretical probability suggests).  Thus, the experimental probability should be considered.

 

Example:  in the early days of computer software, the date/time was used as a seed to produce a pseudo-random number.  However, upon careful computational analysis, it can be determined that this algorithm does not produce a uniform distribution (and is not "fair").