Question

A bag 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?

Answer 1

Answer:

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

$\frac{3}{39}=\frac{1}{13}$

The probability of selecting silver marble is

$\frac{6}{39}=\frac{2}{13}$

The probability of selecting black marble is

$\frac{30}{39}=\frac{10}{13}$

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 = $6(\frac{1}{13})+5(\frac{2}{13})-1$

Expected profit or loss = $\frac{6}{13}+\frac{10}{13}-1$

Expected profit or loss = $\frac{6+10-13}{13}$

Expected profit or loss = $\frac{3}{13}$

Expected profit or loss = 0.23076923

Expected profit or loss ≈ 0.23077

Positive sigh represents the profit.

Therefore the expected profit is $0.23077.