Adice game involves rolling two dice. a player who rolls a 3, 4, 10, 11, or 12 wins 5 points. a player who rolls a 5, 6, 7, 8, or 9 loses 5 points. if the expected value of playing this game is to lose , a player will points by rolling a 2.

The game will lose by 1.94 points .

Solution:

A player who rolls a 3, 4, 10, 11, or 12 wins 5 points and player who rolls a 5, 6, 7, 8, or 9 loses 5 points.

As two dice are rolled hence the total chances are .

The chances of 3 in rolling are (1,2), (2,1)

So the probability of rolling 3 is

The chance of 4 in rolling are (1,3),(3,1), (2,2)

So the probability of rolling 4 is  

The chance of 10 in rolling are (5,5),(4,6), (6,4)

So the probability of rolling 10 is

The chance of 11 in rolling are (5,6),(6,5)

So the probability of rolling 11 is

The chance of 12 in rolling are (6,6)

So the probability of rolling 12 is  

So the total probability of winning is

Hence the probability of losing is

So the expected value of the game

Therefore, the game will lose by 1.94 points