Question

question 6 (5 points)
a bag contains 1 gold marbles, 10 silver marbles, and 21 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?

question 7 (2*5 points)

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is \(1 + 10+21=32\) marbles.

Step2: Calculate the probability of each event

• Probability of getting a gold marble \(P(\text{gold})=\frac{1}{32}\)
• Probability of getting a silver marble \(P(\text{silver})=\frac{10}{32}\)
• Probability of getting a black marble \(P(\text{black})=\frac{21}{32}\)

Step3: Calculate the expected value formula \(E(X)=\sum_{i}x_{i}P(x_{i})\)

Here, \(x_1 = 3\) (value for gold), \(x_2 = 2\) (value for silver), \(x_3=- 1\) (value for black)

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Answer:

\(0.0625\)