Diablo Valley College Biker Dude and Non linear Orders Question It’s a typical Saturday night. You’re at your favorite pub, contemplating the true meaning

Diablo Valley College Biker Dude and Non linear Orders Question It’s a typical Saturday night. You’re at your favorite pub, contemplating the true meaning of infinite cardinalities, when a burly-looking biker plops down on the stool next to you. Just as you are about to get your mind around p(p(R)), biker dude slaps three strange-looking dice on the bar and challenges you to a $100 wager. His rules are simple. Each player selects one die and rolls it once. The player with the lower value pays the other player $100. Naturally, you are skeptical, especially after you see that these are not ordinary dice. Each die has the usual six sides, but opposite sides have the same number on

them, and the numbers on the dice are different, as shown here;

Biker dude notices your hesitation, so he sweetens his offer: he will pay you $105 if you roll the higher number, but you only need pay him $100 if he rolls higher, and he will let you pick a die first, after which he will pick one of the other two. The sweetened deal sounds persuasive since it gives you a chance to pick what you think is the best die, so you decide you will play.

But which of the dice should you choose?

Let us practice the 4 steps modelling method;

1. Die A versus Die B
Step 1: Find the sample space.
Step 2: Define events of interest.
Step 3: Determine outcome probabilities.
Step 4: Compute event probabilities.

1. Die A versus Die B:
Show all above steps and find What is the probability of A winning against B?
2. Die B versus Die C :
Show all steps and find What is the probability of C winning against B?
3. Die C versus Die A:
Show all steps and find What is the probability of A winning against C.
4. Show that A>B>C>A meaning: A beats B beats C beats A.
5. Rolling Twice: Show that AB>C>A meaning: A beats B beats C beats A.
5. Rolling Twice: Show that A 10
8
2
6
6
5
12
10
13
14
10
14
14
18
To compute the number of outcomes where A beats B, we observe that the two rolls of die Aresult in nine equally likely outcomes in a sample space SA in which ….
Repeat the above for two role problem in which the sum of the two roles is used to find the winner.
6. Show that with two roles each turn; the strength of die reverses that is:
A
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