Question

A bag contains 2 gold marbles, 8 silver marbles, and 26 black marbles. Someone offers to play this game: Yourandomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, youlose $1.What is your expected value if you play this game?

Answer 1

The first step is to find the probability for each of the events, which are pick up a gold marble, pick up a silver marble and pick up a black marble:

`\begin{gathered} P(G)=(2)/(36)=(1)/(18) \\ P(S)=(8)/(36)=(2)/(9) \\ P(B)=(26)/(36)=(13)/(18) \end{gathered}`

Now, multiply each of the probabilities by its corresponding reward and find the sum of them to find the expected value:

`\begin{gathered} E=3\cdot(1)/(18)+2\cdot(2)/(9)-1\cdot(13)/(18) \\ E=-0.11 \end{gathered}`

The expected value is -$0.11.