# Prize Winner, Part 3

### Resources for this lesson:

Khalid, Justyce, Andrew, Marissa and Allyson are satisfied with the game. They feel that the probabilities involved in the game make the game challenging, yet contestants do have a chance to win. They decide, based on the probabilities, to award three levels of prizes. They make the following rule sign to accompany the game board.

What’s Behind the Door?

If you can guess the letter behind the door, you win a prize!

Large Prize:
Guess all three doors correctly

Medium Prize:
Guess two doors correctly

Small Prize:
Guess one door correctly

Prize

Probability to Win

Small

$\frac{12}{27}$

Medium

$\frac{6}{27}$

Large

$\frac{1}{27}$

Recall how the game is created and conducted. Khalid, Justyce, Andrew, Marissa and Allyson designed the board so that one of three letters, A – B – C, is placed behind each of the doors. The letters are changed with each contestant to keep the game fair, and the letters behind the doors can repeat. For example, in one round the letter sequence could be C – B – A, and in the next round the letter sequence could be A – A – A.

How would the probabilities for the prizes change, if the letters behind the doors could not repeat?