A bag contains 3 gold marbles, 10 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

A bag contains 4 gold marbles, 10 silver marbles, and 29 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $3. If it costs $1 to play, what is your expected profit or loss if you play this game?

Well, that's quite the colorful game! Let's see if we can make some marble-mania magic happen here. With 3 gold marbles, 10 silver marbles, and 21 black marbles, the odds are definitely not in your favor. But hey, sometimes it's fun to roll the dice and see what happens! Just be careful not to go into "marble madness." Good luck, my friend, and may the marbles be ever in your favor (and not in your pockets)!

To determine whether it is a good idea to play this game, we can calculate the expected value, which is the average amount of money you can expect to win or lose per game.

Step 1: Calculate the probability of selecting each type of marble:

- P(gold) = Number of gold marbles / Total number of marbles = 3 / (3 + 10 + 21) = 3 / 34
- P(silver) = Number of silver marbles / Total number of marbles = 10 / 34
- P(black) = Number of black marbles / Total number of marbles = 21 / 34

Step 2: Calculate the amount of money you can expect to win or lose for each type of marble:

- Amount of money if gold marble is selected: $3
- Amount of money if silver marble is selected: $2
- Amount of money if black marble is selected: -$1

Step 3: Calculate the expected value:

Expected Value = (Amount of money if gold marble is selected) * P(gold) + (Amount of money if silver marble is selected) * P(silver) + (Amount of money if black marble is selected) * P(black)

Expected Value = ($3)(3/34) + ($2)(10/34) + (-$1)(21/34)

Simplifying the equation:

Expected Value = $0.2647 + $0.5882 - $0.6176

Expected Value = $0.2353

Step 4: Conclusion

The expected value of playing this game is $0.2353. Since the expected value is positive, it means that on average, you can expect to win money by playing this game. Therefore, it would be a good idea to play the game.

To determine the expected value of this game, we need to calculate the probability of selecting each type of marble and multiply it by the corresponding amount of money you could win or lose.

There are a total of 3 + 10 + 21 = 34 marbles in the bag.

The probability of selecting a gold marble is 3/34 because there are 3 gold marbles out of 34 total marbles.
The amount you could win if you select a gold marble is $3.

The probability of selecting a silver marble is 10/34 because there are 10 silver marbles out of 34 total marbles.
The amount you could win if you select a silver marble is $2.

The probability of selecting a black marble is 21/34 because there are 21 black marbles out of 34 total marbles.
The amount you would lose if you select a black marble is -$1.

To calculate the expected value, we multiply each probability by the corresponding amount you could win or lose and sum them up:

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

Expected value = (3/34 * $3) + (10/34 * $2) + (21/34 * -$1)

Now, we can calculate the expected value:

Expected value = $0.44

So, the expected value of this game is $0.44.

I don't see a question, but the expected value

E = 3(3/34) + 2(10/34) - 1(21/34) = 4/17 = $0.24