Question

A dice 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.

Answer 1

Answer:

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 $(6\times6) = 36$.

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

So the probability of rolling 3 is $\frac{2}{36}$

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

So the probability of rolling 4 is  $\frac{3}{36}$

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

So the probability of rolling 10 is $\frac{3}{36}$

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

So the probability of rolling 11 is $\frac{2}{36}$

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

So the probability of rolling 12 is $\frac{1}{36}$  

So the total probability of winning is $\left(\frac{2}{36}+\frac{3}{36}+\frac{3}{36}+\frac{2}{36}+\frac{1}{36}\right)=\frac{11}{36}$

Hence the probability of losing is $\left(1-\frac{11}{36}\right)=\frac{25}{36}$

So the expected value of the game $=\left(\frac{11}{36}\right) \times 5+\left(\frac{25}{36}\right) \times(-5)=\left(\frac{55}{36}-\frac{125}{36}\right)=\left(-\frac{70}{36}\right)=-1.94$

Therefore, the game will lose by 1.94 points

Answer 2

player will "WIN"  "5" points by rolling a 2.

Just took the test on Edmentum this is correct.