I seriously on this problem THANX

[braceface084]

I seriously need help on this problem...THANX :)

Die A has four 9's and two 0's on its faces. Die B has four 3's and two 11's on its faces. when either of these dice is rolled, each face has an equal chance of landng on top. two players are going to play a game. the first player selects a die and rolls it. the second player rolls the remaining die. the winner is the player whose die has the higher number on top.

A) suppose you are the first player and you want to win the game. which die would you select and why

B) Suppose the player using die A receives 45 tokens each time he or she wins the game. how many tokens must the player using die B receive each time he or she wins in order for this to be a fair game?

i really don't know how to start this.

any help is appreciated. thanks in advance

 

[dotman]

Hello,

I think the first thing you need to look at are the probabilities of rolling each value, and what effect that will have for the game.

For instance, if you select Die B, what is the chance you'll roll a 3? Furthermore, if you roll a 3, what is the chance that it will win the game? (be higher than Die A's roll?)

What is the formula for probability?

 

[ogb p]

As a scientist, my response would be to approach this problem using probability and statistics.

A) To determine which die has a higher chance of winning, we can calculate the probability of rolling a higher number on each die. For Die A, the probability of rolling a higher number is 4/6 or 2/3. For Die B, the probability is 2/6 or 1/3. Therefore, Die A has a higher chance of winning and as the first player, I would select Die A to increase my chances of winning the game.

B) To make the game fair, the expected value of winning for both players should be the same. Since the player using Die A receives 45 tokens per win, the expected value for that player is 45 tokens. To calculate the expected value for the player using Die B, we can set up the following equation:

(1/3) * x = 45

Solving for x, we get x = 135. This means that the player using Die B should receive 135 tokens per win in order for the game to be fair.

In conclusion, using probability and expected value, we can determine which die has a higher chance of winning and how many tokens should be given to the player using the other die in order for the game to be fair. I hope this helps you in solving the problem.