A "probabilistic" inequality

honestly there just aren't that many possibilities. for each values of x, there are 5 options for y.

  • X = 0, there is 4 options where y is higher than x.
  • X = 1, there is 3 options where y is higher than x.
  • X = 2, there is 2 options where y is higher than x.
  • X = 3, there is 1 options where y is higher than x.

That gives you:

4/5+3/5+2/5+1/5

To get the probabilities of an event happening, you have to divide the options where it happens by the sum of all the options.

There are 4 options of x. For each of these, there is 5 options for y.

This gives us a total of

(4/5+3/5+2/5+1/5)/(5*4).

Course there is simpler ways of calculating this in this case, but if you ever want to check your answer, bruteforcing is an option.

/r/compsci Thread Link - i.redd.it