A bag contains 1 gold marbles, 10 silver marbles, and 29 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?

Well, let's do the math and find out!

The probability of selecting a gold marble is 1 out of 40 (since there is 1 gold marble out of a total of 40 marbles). So, the expected value if you win $4 is:

(1/40) * $4 = $0.10

The probability of selecting a silver marble is 10 out of 40. So, the expected value if you win $2 is:

(10/40) * $2 = $0.50

The probability of selecting a black marble is 29 out of 40. So, the expected value if you lose $1 is:

(29/40) * -$1 = -$0.725

Now, let's add up the expected values:

$0.10 + $0.50 - $0.725 = -$0.075

So, the expected value of playing this game is -$.075. Oops, looks like it's a clownish proposition! Better hold onto your money!

To calculate the expected value, we need to multiply the value of each outcome by its corresponding probability, and then sum all the results. Let's calculate it step by step:

Step 1: Calculate the probability of drawing each type of marble.
- Probability(Gold) = Number of Gold / Total number of marbles = 1 / (1 + 10 + 29) = 1/40
- Probability(Silver) = Number of Silver / Total number of marbles = 10 / (1 + 10 + 29) = 10/40 = 1/4
- Probability(Black) = Number of Black / Total number of marbles = 29 / (1 + 10 + 29) = 29/40

Step 2: Calculate the value of each outcome.
- Value(Gold) = $4
- Value(Silver) = $2
- Value(Black) = -$1

Step 3: Calculate the expected value.
Expected Value = Probability(Gold) * Value(Gold) + Probability(Silver) * Value(Silver) + Probability(Black) * Value(Black)
Expected Value = (1/40) * 4 + (1/4) * 2 + (29/40) * -1

Calculating the above expression, we get:

Expected Value = 0.1 + 0.5 - 0.725

Therefore, the expected value of playing this game is approximately -$0.125 (or -$0.13 rounded to two decimal places). This means that on average, you would lose around $0.13 per game if you continue to play this game in the long run.

To find the expected value, we need to multiply the possible outcomes by their respective probabilities and sum them up.

First, let's calculate the probabilities of selecting each type of marble:

Probability of selecting a gold marble:
Since there is only 1 gold marble out of a total of 40 marbles, the probability of selecting it is 1/40.

Probability of selecting a silver marble:
There are 10 silver marbles out of a total of 40 marbles, so the probability of selecting one is 10/40, which simplifies to 1/4.

Probability of selecting a black marble:
There are 29 black marbles out of a total of 40 marbles, so the probability of selecting one is 29/40.

Now let's calculate the expected value:

Expected value = (Probability of gold marble) * (Value for gold marble) + (Probability of silver marble) * (Value for silver marble) + (Probability of black marble) * (Value for black marble)

Expected value = (1/40) * $4 + (1/4) * $2 + (29/40) * (-$1)

Simplifying this equation gives:

Expected value = $0.1 + $0.5 - $0.725

Expected value = -$0.125

So, if you play this game multiple times, you can expect to lose an average of $0.125 per game.

(1/40)(4) + (10/40)(2) - (29/40)(1) = -5/40