Question

A person plays a game where he blindly picks a colored chip from a container. There are 20 chips in the container: 5 red, 11 green, and 4 blue. He gets $1 for a red chip, nothing for a green chip, and he has to pay $1.25 if he picks a blue chip. This is a fair game.

Answer 1

yes it is because the person has a 16 out 20 chance of walking away with $1 or nothing but there's still a 20% chance that they can pick a blue one 

Answer 2

Answer: Hello there!

here we have 20 chips, where 4 are blue, 5 are red and 11 green.

Now we want to see if the game is fair or not, to see this, let's see the expected value of the game:

the expected value is defined as E = ∑pₙxₙ

where pₙ is the probability of the event xₙ

Here we have 3 events:

win 1 dollar, where the probability is the number of red chips divided by the total amount of chips 5/20

win 0 dollars, whit a probability of 11/20

loss of 1.25 dollars, with a probability of 4/20

then the expected value is:

E = ($1*5 + $0*11 - $1.25*4)/20 = $0

Then the expected value is 0 dollars, this means that the game is not biased in any direction.

Then, the game is a fair game.