Question

A game is played as follows:

A coin is flipped 3 times.

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.

In two or more sentences, explain whether or not the game is fair.

Answer 1

No the game isn't fair. The probability of heads to tails is uneven. 

Answer 2

The game is not fair.

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
`(1)/(8)` 5

1
`(3)/(8)` -5

2
`(3)/(8)` -4

3
`(1)/(8)` 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,

`5 * (1)/(8) -5* (3)/(8)- 4*(3)/(8) + 4* (1)/(8)`

`(5)/(8) -(15)/(8)- (12)/(8) +(4)/(8) \\=(-18)/(8)`

Thus, the expected value is not 0.

Therefore, the game is not fair.