Answer:
The game is not fair.
Step-by-step explanation:
Consider the provided information.
It is given that A game is played as follows:
Consider the sample space if coin is flipped 3 times.
(HHH), (HHT), (HTH), (THH), (TTH), (THT), (HTT), (TTT)
If 3 heads come up, then you win $5.
If 2 heads come up, then you lose $5.
If 1 head comes up, then you lose $4.
If no heads (all tails) come up, then you win $4.
Now make the table:
No of heads(x) Probability (P) win($)
0 [tex]\frac{1}{8}[/tex] 5
1 [tex]\frac{3}{8}[/tex] -5
2 [tex]\frac{3}{8}[/tex] -4
3 [tex]\frac{1}{8}[/tex] 4
The expected value for a 1 unit bet can be calculated by Multiply the chance of winning by the bet value in order to know the expected gain.
Therefore,
[tex]5 \times \frac{1}{8} -5\times \frac{3}{8}- 4\times\frac{3}{8} + 4\times \frac{1}{8}[/tex]
[tex]\frac{5}{8} -\frac{15}{8}- \frac{12}{8} +\frac{4}{8} \\=\frac{-18}{8}[/tex]
Thus, the expected value is not 0.
Therefore, the game is not fair.
