Respuesta :
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
[tex]\frac{3}{39}=\frac{1}{13}[/tex]
The probability of selecting silver marble is
[tex]\frac{6}{39}=\frac{2}{13}[/tex]
The probability of selecting black marble is
[tex]\frac{30}{39}=\frac{10}{13}[/tex]
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 = [tex]6(\frac{1}{13})+5(\frac{2}{13})-1[/tex]
Expected profit or loss = [tex]\frac{6}{13}+\frac{10}{13}-1[/tex]
Expected profit or loss = [tex]\frac{6+10-13}{13}[/tex]
Expected profit or loss = [tex]\frac{3}{13}[/tex]
Expected profit or loss = 0.23076923
Expected profit or loss ≈ 0.23077
Positive sigh represents the profit.
Therefore the expected profit is $0.23077.
