The game of heads up is played by flipping two coins. If they both land heads up, you win $8. If only one lands heads up, you win $14. If no coins land heads up, you win $0. If you pay $6 to play the game each time the coins are flipped, is the game a fair game? Why or why not?

The game of heads up is played by flipping two coins. The game is a fair gameSolution:Given that , the game of heads up is played by flipping two coins.  If they both land heads up, you win $8.  And If only one lands heads up, you win $14.  And If no coins land heads up, you win $0.  We have to pay $6 to play the game each time the coins are flipped,  Then we have to find is the game a fair game Now, we say a thing is fair if it is favorable for us. From players view, to say the game is fair, we have to get money.  Now, if we see When we pay $6, we will lose it only when no heads are up as we get $0 in that condition. But we will get 14 – 6 = $8 when one head turns up and 8 – 6 = $2 when both heads are up. Now, number of outcomes for losses = 1 (tail – tail condition) Probability = [tex]\frac{1}{4}[/tex]And number of outcomes for winnings = 3 (head - tail, tail – head and head – head conditions) Probability = [tex]\frac{3}{4}[/tex]Clearly we can say that, chances of winnings are more. Hence, it is an fair game.