Calculation of probability with arithmetic mean of random variables

There are 4 people, each of whom has one deck of cards with 500 cards that are numbered from 1 to 500 with no duplicates.

Each person draws a card from his deck and I would like to calculate the probability of the event that "the arithmetic mean of the number on the 4 cards is 405".

How to make that?

Some explanation is welcome.
Last edited:


Well-Known Member
I assume you mean the average of the 4 cards equals to 405?

guideline: the probability is the number of possible events meet the criteria divided by the total number of possible events.

Example the probability of getting an even number in a die.
the number of possible events meets the criteria: 3 (2,4,6)
the number of possible events: 6 (1,2,3,4,5,6)