Question

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?

Answer 1

The game of heads up is played by flipping two coins. The game is a fair game

Solution:

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 = $\frac{1}{4}$

And number of outcomes for winnings = 3 (head - tail, tail – head and head – head conditions)

Probability = $\frac{3}{4}$

Clearly we can say that, chances of winnings are more.

Hence, it is an fair game.