Question: (2 points)

You and two friends are on a game show. Each of you enters the studio with a hat on your head. There are two colors of hats: red and blue. They are assigned randomly. so each person has a 50% chance of a red hat and a 50% chance of a blue hat. Each person can see the hats of the two other people, but they can't see their own hat. Each person can either try to guess the color of his or her own hat or pass. All three of you do it simultaneously. so there is no way to base your guess on the guesses of your friends. If nobody guesses incorrectly and at least one person guesses correctly, then you all share a big prize. Otherwise you all lose. If everybody randomly guesses and nobody passes what is the probability that you will win?

Since you are all friends, and you all know how the game works. you develop a strategy with your friends before the show to maximise your probability of winning.

(Note: if your strategy requires a particular person to speak regardless of what hat colours you all see then that person is you.

In cases where both colours are equally attractive then you will pick red.)

When you walk onto the stage you can see that both of your friends have red hats on. What colour should you guess?

1. Red
2. Blue
3. Stay silent

When you walk onto the stage you can see that one of your friends has a red hat on and the other friend has a blue hat on.

What colour should you guess?

1. Red
2. Blue
3. Stay Silent

What is the probability that you will win using the best strategy?

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document