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Station 1 B

This document contains a series of questions about the probabilities of winning simple dice games. In the first game, two dice are rolled and the player with the highest number wins, with possibilities of 1-4 for player 1 and 5-6 for player 2. In an extension, two dice are rolled and multiplied, with multiples of 6 winning for one player and non-multiples winning for the other. The document prompts the reader to calculate probabilities and determine which player is favored in each game.

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142 views4 pages

Station 1 B

This document contains a series of questions about the probabilities of winning simple dice games. In the first game, two dice are rolled and the player with the highest number wins, with possibilities of 1-4 for player 1 and 5-6 for player 2. In an extension, two dice are rolled and multiplied, with multiples of 6 winning for one player and non-multiples winning for the other. The document prompts the reader to calculate probabilities and determine which player is favored in each game.

Uploaded by

api-447408766
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 4

Name: ______________________

Date: ________________________

Station #1 – Castaway

You and a fellow castaway are stranded on a desert island, playing dice for the
last banana. You’ve agreed on two rules:
You’ll roll two dice:
1) If the biggest number is 1, 2, 3, or 4, player 1 wins.
2) If the biggest number is 5, or 6, player 2 wins.

Answer the following questions to demonstrate which player is more likely to


win.

1) At first glance, who do you think is more likely to win: player 1, or player
2?

2) Are the events (event 1 being rolling the first die, and event 2 being
rolling the second die) independent or dependent events? Why?

3) Using the basic counting principle, determine how many possible


outcomes there are when rolling two dice.

There are ______________ possible outcomes.


4) The table below shows the possible outcomes for the first roll (columns)
and the second roll (rows). Fill in the table with who wins for each
combination.

For example, if a 1 is rolled on the first roll, and a 1 is rolled on the second
roll, player 1 wins. Fill out the rest of the table.

1 2 3 4 5 6

1 Player 1
Wins
2

5) Out of all the possible combinations, how many give the victory (i.e. the
banana) to player 1?

6) Out of all the possible combinations, how many give the victory (i.e. the
banana) to player 2?

7) What would be a fairer set of rules, when rolling two dice, where both
players have a more equal probability of winning?
Extension Question:

Let’s look at the probabilities of another game. This is how it works: we roll two
dice and calculate the multiplication of the two numbers we rolled. --If it is a
multiple of 6, I win --If it is not a multiple of 6, you win. Here is an example: If you
get 3 and 4, the multiplication is 12. Twelve is a multiple of 6, so I win!

1) Which player would win if you get 2 and 5 in the dice? Me or you?

2) Which player would win if you get 4 and 2 in the dice?

3) Which player would win if you get 1 and 6 in the dice?


4) The table below shows the possible outcomes for the first roll (columns)
and the second roll (rows). Fill in the table with who wins for each
combination.

For example, if a 1 is rolled on the first roll, and a 1 is rolled on the second
roll, you win because 1x1 = 1 is not a multiple of 6. Fill out the rest of the
table.

1 2 3 4 5 6

5) Calculate the probability you win the game vs. I win the game. Who has
the higher probability of winning the game?

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