Question

In a board game, you roll a die to win or lose points, depending on the outcome. The outcomes follow this probability distribution.
If a player can only win by accumulating 20 points, which of the following best describes the fairness of the game?

Answer 1

A, it's not fair because the chance to lose points far outweighs the chance to gain points

Answer 2

Answer with explanation:

→Total faces on the dice and marked numbers =6={1,2,3,4,5,6}

If you are rolling the dice and getting number 1 and 5 , you win 4 and 6 points respectively.

And, If you roll the dice and getting number 2,3,4 and 6 , you loose -5  points .

→→So,suppose the dice is rolled 6 times, and considering each outcome to be equally likely

         then you loose more points than gaining which is equal to

   = 4+(-5)+(-5)+(-5)+6+(-5)

   =10-20

   = -10

And, Average

$=\frac{-10}{5}\\\\= -2$

So, if number of outcomes are equally likely, you can't accumulate 20 points.

Option B:→ It is not a fair game because weighted average is Negative.