chance of gold = 1/36
chance of silver = 9/36
chance of black = 26/36
1/36 * 3 + 9/36 * 2 - 26/36 * 1
3/36 + 18/36 - 26/36
= -5/36
:(
chance of silver = 9/36
chance of black = 26/36
1/36 * 3 + 9/36 * 2 - 26/36 * 1
3/36 + 18/36 - 26/36
= -5/36
:(
To do this, we need to multiply the value of each outcome by its corresponding probability and then sum them all up. So, let's crunch some numbers!
The probability of picking a gold marble is 1 out of 36, since there is only one gold marble out of the total 36 marbles in the bag. So, the expected value for a gold marble is (1/36) * $3 = $0.08.
The probability of picking a silver marble is 9 out of 36, giving it a probability of 1/4. Thus, the expected value for a silver marble is (1/4) * $2 = $0.50.
Now, the probability of picking a black marble is 26 out of 36, or 13/18. Thus, the expected value for a black marble is (13/18) * (-$1) = -$0.72.
Now we add up all the expected values: $0.08 + $0.50 - $0.72 = -$0.14.
So, my friend, the expected value of this game is that you would lose $0.14 on average. Oof, tough luck! But remember, it's all just numbers, so don't be too upset.
Let's calculate the probability of drawing each type of marble first:
The probability of drawing a gold marble is 1 out of a total of 1 + 9 + 26 = 36 marbles, which can be written as 1/36.
The probability of drawing a silver marble is 9 out of 36 marbles, which can be written as 9/36 or 1/4.
The probability of drawing a black marble is 26 out of 36 marbles, which can be written as 26/36 or 13/18.
Now, let's calculate the expected value:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = [(1/36) * $3] + [(9/36) * $2] + [(26/36) * (-$1)]
Expected value = $0.08 + $0.50 - $0.72
Expected value = $0.58 - $0.72
Expected value = -$0.14
Therefore, the expected value if you play this game is -$0.14.
First, we need to determine the probability of drawing each type of marble. There are a total of 1 + 9 + 26 = 36 marbles in the bag, and only 1 of them is gold. Therefore, the probability of drawing a gold marble is 1/36.
Similarly, there are a total of 9 silver marbles, so the probability of drawing a silver marble is 9/36 or 1/4.
Finally, there are 26 black marbles, so the probability of drawing a black marble is 26/36 or 13/18.
Next, we calculate the expected value by multiplying each outcome by its probability:
E(X) = (3 * 1/36) + (2 * 9/36) + (-1 * 26/36)
E(X) = 3/36 + 18/36 - 26/36
E(X) = -5/36
Therefore, the expected value of playing this game is -5/36, which means that on average, you can expect to lose approximately $0.14 each time you play.