Answer:
42 cents
Step-by-step explanation:
Data provided in the question:
Random variable i.e gain with values 3,2,1,-1.
Now,
The corresponding probabilities will be as follows:
[tex]P(3)=(\frac 16)^{3}[/tex]
[tex]P(2)=3\times(\frac 16)^{3}[/tex]
[tex]P(1)=3\times(\frac 16)^{3}[/tex]
[tex]P(-1)=1-7(\frac 13)^{3}[/tex]
Expected gain = [tex]3\times(\frac 16)^{3}+2\times3\times(\frac 16)^{3}+1\times3\times(\frac 16)^{3}-1\times\left(1-7\times(\frac 13)^{3}\right)[/tex]
Expected gain = [tex](\frac 13)^{3}[3+6+3-(0.7407)][/tex]
[tex]=(\frac 16)^{3}[11.2593]=0.4170[/tex]
≈ 42 cents
