Fair Game: Choosing the Best Die for Probability and Statistics

[braceface084]

i was put in this class and I am 14 and i seriously need some help on this topic


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. for a, i would think that, logically, die B would be better to choose but i don't know how to prove that statistically (even if it's right in the first place)

any help is appreciated. thanks in advance

 

[Dick]

Figure out what the probability of winning is. The only way die A wins is if A rolls 9 and B rolls 3. What's the probability of each of those events and of both of them occurring together?

 

[Skins]

I could show you how to do it now but that would take away the fun and the learning. Look at the ways there are to win if Die A is selected. Then look at the ways to win if Die B is selected. Think of those ways in terms of events events. Determine the probabilities of the events. Think of what kind of events they are and apply the basic rules of probability that you learned. Give it a try and see how you do.