Question

A bag contains 3 gold marbles, 8 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.

Answer 1

To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.

Let's start by calculating the probability of selecting each type of marble:

Probability of selecting a gold marble: 3/34

Probability of selecting a silver marble: 8/34

Probability of selecting a black marble: 23/34

Now, let's calculate the expected value of playing the game:

E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)

E(x) = $0.26

So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.