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

This game is not fair. No one will know wha their going to get. It is a game of probability

Answer 2

Explanation:

Given that 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.

No of heads X 0 1 2 3

Prob p
`(1)/(8) , (3)/(8) ,(3)/(8) ,(1)/(8)`

Win 5 -5 -4 4

Expected win of the game = Sum of win amount * Prob

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

Since expected value is not 0 the game is not fair.