Answer to Question #310211 in Statistics and Probability for dino

Question

You play a game with two six-sided dice. If you roll a sum of 5 or 7, you win ₱400. If you

roll a sum of 6 or 8, you win ₱300. If you roll a sum of 11 or 12, you win ₱200. However,

you lose ₱250 for anything else. If you continue to play the game, how much do you

expect to win or lose in the game? Will you encourage your friend to play that kind of

game? Why or why not?

Answer 1

The rolls which win 400: (1,4),(1,6),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(6,1) – total 10 of 36 variants

The rolls which win 300:

$\left( 1,5 \right) ,\left( 2,4 \right) ,\left( 2,6 \right) ,\left( 3,3 \right) ,\left( 3,5 \right) ,\left( 4,2 \right) ,\left( 4,4 \right) ,\left( 5,1 \right) ,\left( 5,3 \right) ,\left( 6,2 \right)$ - total 10 of 36 variants

The rolls which win 200:

$\left( 5,6 \right) ,\left( 6,5 \right) ,\left( 6,6 \right)$ - total 3 of 36 variants

Other 36-10-10-3=13 variants lose 250.

The expectation is

$EX=400\cdot \frac{10}{36}+300\cdot \frac{10}{36}+200\cdot \frac{3}{36}-250\cdot \frac{13}{36}=120.833$

The expectation is positive, I will encourage my friend to play.