Answer to Question #161684 in Statistics and Probability for vergel

Question

 In the same carnival, there is a similar game of chance. The game involves a small bag containing 30 marbles where 12 are green, 8 are yellow, and the rest are brown. You win Php 20.00 if you are able to draw a green marble, and you win Php 10.00 if you are able to draw a yellow marble. You lose Php 30.00 if you are able to draw a brown ball. If you continue to play the game, how much do you expect to win or lose in the game?

Answer 1

Let $X=$ the amount of money received

$$P(green)=\dfrac{12}{30}=\dfrac{2}{5}$$

$$P(yellow)=\dfrac{8}{30}=\dfrac{4}{15}$$

$$P(brown)=\dfrac{10}{30}=\dfrac{1}{3}$$ $$\begin{matrix} x & 20 & 10 & -30 \\ p & \dfrac{2}{5} & \dfrac{4}{15} & \dfrac{1}{3} \end{matrix}$$

$$E(X)=\sum_ix_ip(x_i)=20(\dfrac{2}{5})+10(\dfrac{4}{15})+(-30)(\dfrac{1}{3})=$$

$$=\dfrac{2}{3}$$

I expect to win Php 0.67 in the game.