In the same carnival there is a similar game of chance. The game involves a small bag containing 30 marbles where 12 are green and 8 are yellow and the rest are brown. You win 20 pesos if you are able to draw green marble and you win 10 pesos if you are able to draw a yellow marble. You lose 30 pesos if you are able to draw brown ball. H much do you expect to win or lose if you play the game twice?
expected return per play
... (20 * 12/30) + (10 * 8/30) - (30 * 10/30)
To calculate the expected value of playing the game twice, we need to determine the probability of winning and losing in each draw and multiply that by the amount won or lost.
In the given scenario, there are 30 marbles in total, with 12 being green, 8 being yellow, and the remaining being brown.
First, let's calculate the probability of drawing a green marble in one draw. The probability can be calculated by dividing the number of green marbles (12) by the total number of marbles (30):
Probability of drawing a green marble = Number of green marbles / Total number of marbles = 12/30 = 2/5
Similarly, the probability of drawing a yellow marble can be calculated as:
Probability of drawing a yellow marble = Number of yellow marbles / Total number of marbles = 8/30 = 4/15
To find the probability of drawing a brown marble, we subtract the sum of the probabilities of drawing a green and yellow marble from 1:
Probability of drawing a brown marble = 1 - (Probability of drawing a green marble + Probability of drawing a yellow marble) = 1 - (2/5 + 4/15) = 7/15
Now, let's calculate the expected value for each scenario:
Case 1: Drawing a green marble
Expected value = (Amount won per green marble)*(Probability of drawing a green marble) = 20 pesos * (2/5) = 8 pesos
Case 2: Drawing a yellow marble
Expected value = (Amount won per yellow marble)*(Probability of drawing a yellow marble) = 10 pesos * (4/15) = 2.67 pesos (rounded to the nearest cent)
Case 3: Drawing a brown marble
Expected value = (Amount lost per brown marble)*(Probability of drawing a brown marble) = -30 pesos * (7/15) = -14 pesos
To calculate the overall expected value over two draws, we simply add the individual expected values:
Total expected value = (Expected value for drawing a green marble + Expected value for drawing a yellow marble + Expected value for drawing a brown marble) * Number of draws
Total expected value = (8 pesos + 2.67 pesos - 14 pesos) * 2 draws = -3.33 pesos (rounded to the nearest cent)
Therefore, you can expect to lose around 3.33 pesos if you play the game twice.