Abag contains 3 gold marbles, 6 silver marbles, and 30 black marbles. the rules of the game are as follows: you randomly select one marble from the bag. if it is gold, you win $6, if it is silver, you win $5. if it costs $1 to play, what is your expected profit or loss if you play this game?

The expected profit is $0.23077.

Step-by-step explanation:

From the given information it is clear that

Gold marbles = 3

Silver marbles = 6

Black marbles = 30

Total number of marbles = 3+6+30=39

The probability of selecting gold marble is

The probability of selecting silver marble is

The probability of selecting black marble is

It is given that If it is gold, you win $6, if it is silver, you win $5. If it costs $1 to play. Then the expected profit is

Expected profit or loss = 6(Probability of gold marble)+5(Probability of silver marble)-1

Expected profit or loss =

Expected profit or loss =

Expected profit or loss =

Expected profit or loss =

Expected profit or loss = 0.23076923

Expected profit or loss ≈ 0.23077

Positive sigh represents the profit.

Therefore the expected profit is $0.23077.