I don't see a question, but the expected value
E = 3(3/34) + 2(10/34) - 1(21/34) = 4/17 = $0.24
E = 3(3/34) + 2(10/34) - 1(21/34) = 4/17 = $0.24
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.
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.