MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one 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. What is your expected value if you play this game? $\_\_\_\_ [Submit Question]
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Transcribed Image Text:A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one 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. What is your expected value if you play this game? $\_\_\_\_ [Submit Question]
**Question 12** A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one 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. What is your expected value if you play this game? \[ \text{\$} \_\_ \] [Submit Question Button] --- **Explanation for Educational Purposes:** To calculate the expected value of this game, follow these steps: 1. **Determine the Total Number of Marbles:** \[ 2 \text{ (gold)} + 6 \text{ (silver)} + 23 \text{ (black)} = 31 \text{ marbles in total} \] 2. **Calculate the Probability of Each Marble:** - Probability of drawing a gold marble: \( \frac{2}{31} \) - Probability of drawing a silver marble: \( \frac{6}{31} \) - Probability of drawing a black marble: \( \frac{23}{31} \) 3. **Determine the Expected Value:** Use the formula for expected value: \[ EV = (\text{Probability of Gold} \times \text{Value of Gold}) + (\text{Probability of Silver} \times \text{Value of Silver}) + (\text{Probability of Black} \times \text{Value of Black}) \] \[ EV = \left(\frac{2}{31} \times 3\right) + \left(\frac{6}{31} \times 2\right) + \left(\frac{23}{31} \times -1\right) \] 4. **Calculate the Expected Value:** - Contribution from gold marbles: \(\frac{2}{31} \times 3 = \frac{6}{31}\) - Contribution from silver marbles: \(\frac{6}{31} \times 2 = \frac{12}{31}\) - Contribution from black marbles: \(\frac{23}{31} \times -1 = -\frac{23}{31}\) \[ EV = \frac{6}{31} + \frac{12}{31} -
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Transcribed Image Text:**Question 12** A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one 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. What is your expected value if you play this game? \[ \text{\$} \_\_ \] [Submit Question Button] --- **Explanation for Educational Purposes:** To calculate the expected value of this game, follow these steps: 1. **Determine the Total Number of Marbles:** \[ 2 \text{ (gold)} + 6 \text{ (silver)} + 23 \text{ (black)} = 31 \text{ marbles in total} \] 2. **Calculate the Probability of Each Marble:** - Probability of drawing a gold marble: \( \frac{2}{31} \) - Probability of drawing a silver marble: \( \frac{6}{31} \) - Probability of drawing a black marble: \( \frac{23}{31} \) 3. **Determine the Expected Value:** Use the formula for expected value: \[ EV = (\text{Probability of Gold} \times \text{Value of Gold}) + (\text{Probability of Silver} \times \text{Value of Silver}) + (\text{Probability of Black} \times \text{Value of Black}) \] \[ EV = \left(\frac{2}{31} \times 3\right) + \left(\frac{6}{31} \times 2\right) + \left(\frac{23}{31} \times -1\right) \] 4. **Calculate the Expected Value:** - Contribution from gold marbles: \(\frac{2}{31} \times 3 = \frac{6}{31}\) - Contribution from silver marbles: \(\frac{6}{31} \times 2 = \frac{12}{31}\) - Contribution from black marbles: \(\frac{23}{31} \times -1 = -\frac{23}{31}\) \[ EV = \frac{6}{31} + \frac{12}{31} -
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