Help explain (answer + question given)

[rapid badger]

Specifically section b)

Picture below

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[rapid badger]

Section b) I do not understand how they got 2/127.

I used 1/2 x 1/2 x 1/32 to attempt to solve

Same issue with section c) but if b) is explained I will hopefully get it

[old sundial]

could you send the whole problem?

[rapid badger]

Ah, forgot about that yes

[old sundial]

👍

[rapid badger]

Oh crack

Sorry, not sure how to flip it

[old sundial]

,rotate

[rapid badger]

Oh ty for helping, just checked ur profile you’re meant to be off relaxing DX

[old sundial]

no

anyways

[rapid badger]

Wait no as in you won’t help explain or no to the relax part .-.

[old sundial]

relax

a true warrior never sleeps

[rapid badger]

Oh ok, ty for helping

[old sundial]

anyways

okay, so you understand the rationale behind part a)

[rapid badger]

Sort of

[old sundial]

what do you not understand?

its kind of foundational to setup for the next questions

[rapid badger]

Ah, I c

[rapid badger]

I didn’t do it the way the solution does, using R in a set position and then getting K’s probability

[old sundial]

Also, what does "not well answered" mean? the explanation or the answer?

[rapid badger]

I’m not sure, they kinda shoved the worksheets to us with the answers. Which is why I’m so confused

[old sundial]

ah.

[rapid badger]

I understand the logic behind a) but if I tried to answer a question using that logic I’d probably fail

[hushed sorrel]

While I do not want to overcomplicate explanations, the key is kind of poop

[rapid badger]

Ah sh*t then

[old sundial]

if the answer is incorrect then what would be the point of the thing, you know?

[hushed sorrel]

The rationale is not that well formulated for how demanding they seem to be

[rapid badger]

I don’t know what the correct answer is if that is not, I was assuming that meant the answer was correct but they would deduct marks based on reasoning

[old sundial]

yeah, but we cant really assume things with grading

oh well

i can attempt at this problem to see what i get

[rapid badger]

So is this impossible to figure out

[rapid badger]

Yes please, thank you so much TwT

[hushed sorrel]

In terms of rationale, you can see the events to compute the probability as intersections of independent events

Or perhaps conditional to another

Which would justify multiplying a bunch of stuff

The reasoning part of the problem is to find out which events and to give reasonable justifications for their independence

(Or dependence)

[rapid badger]

Ah, well I suck at proof / evidence

[old sundial]

huh.

im still confused as to why the probability of winning is not 1/2

[rapid badger]

Do you think making a tree diagram on a much smaller scale would help

[rapid badger]

It is?

[old sundial]

hmm.

[hushed sorrel]

The pronability of a player winning a match is 1/2

[rapid badger]

A) is referring to the probability of R and K facing each other in the first round

[old sundial]

i should feel like you do probability of choosing spots multiplied by winning chances

[rapid badger]

Sorry, must be confusing since the answers and question are separate

[old sundial]

which here would be 3/128x1/2x1/2

[rapid badger]

Where did the 3 come from?

[old sundial]

3 positions to choose from

you have R at any given

[rapid badger]

Yep

[old sundial]

then K must be in the adjacent box

[rapid badger]

Yep

[old sundial]

so in 2 specific spots

thus (1+2)/128 spots avaliable is 3/128

that is what i deduced

[rapid badger]

Where did the final 1 come from

[old sundial]

?

[rapid badger]

Oh wait nvm

K can be on either side of R

[old sundial]

i feel like this is the most logical answer but i cant double check

maybe

ah.

[hushed sorrel]

Excluding R, there are 127 slots remaining, and K can be put in two of those 127 for a valid configuration

[old sundial]

4 spots to choose from.

[hushed sorrel]

So that explains the 2/127

[old sundial]

i see

but wouldn't it be 4?

[rapid badger]

Oh, I kinda get it

[old sundial]

because of the either side

[hushed sorrel]

No

[old sundial]

im overcomplicating it

lmfoa

[hushed sorrel]

No you are getting that part wrong

You can try to draw the tree

[old sundial]

i did

[hushed sorrel]

So there is only one adjacent match next to Ryu's match

[rapid badger]

Thinking of just making a smaller tree diagram with 16 participants and seeing the probability to understand where the heck this is going wrong .-.

[rapid badger]

Can send? I would love to see a reference

[hushed sorrel]

So you have three independent events to consider

[old sundial]

its just 6 circles lol

[hushed sorrel]

• is the configuration valid?
• does Ryu win?
• does Ken win?

[rapid badger]

Circles?

[hushed sorrel]

Compute their individual probabilities, and multiply them for the probability of the intersection of those events

[old sundial]

maybe im being stupid but why

[rapid badger]

What does configuration refer to?

I did not learn that term

[hushed sorrel]

The configuration of the players

There are configurations where Ryu will never be able to face Ken in the second match

e.g. they fight in the first round, or they are too far apart

[rapid badger]

I c

And how do you check if the configuration is valid?

[hushed sorrel]

So you need to find all the configurations that can even allow Ryu and Ken to make it together to the second match

[hushed sorrel]

We explained that a bit earlier

[rapid badger]

Ah, I’ll scroll up then

[hushed sorrel]

A configuration is valid when Ken is fighting in the adjacent match to Ryu's first match

[rapid badger]

I c

[old sundial]

but how come there are not 2 adjacent matches

i.e. 4 slots avaliable

[hushed sorrel]

Let's make a smaller example with 8 players

[rapid badger]

For part b) ?

[old sundial]

drew it

[rapid badger]

I’m very lost

[hushed sorrel]

So the tree looks like:

     Winner
F1              F2

SF1 Sf2 SF3 SF4
P1 P2 .... .... ........ P8

[rapid badger]

Yep

[old sundial]

i just drew circles but yeah

[hushed sorrel]

Now if Ryu is, say, P3

The only adjacent match is P1 vs P2

P5 vs P6 is not adjacent

[rapid badger]

Yes

[hushed sorrel]

Since they're in a different half

Starting from the root of the tree

[old sundial]

what

[rapid badger]

Ok following so far

[hushed sorrel]

Ryu will never be able to face P5 or P6 in the semi finals

[old sundial]

maybe im seeing it different than you

1 sec

[rapid badger]

How come?

[hushed sorrel]

Since P5 and P6 can only advance to SF3

And SF3 does not fight against SF2

No matter the outcome

[rapid badger]

I’m reading the question again and it says that “the competitors for each round are randomly paired from the pool of those who remain”

I.e, you can win as P7 and be matched with P3 in SF

[hushed sorrel]

Oh so they are randomly shuffled again?

[rapid badger]

Yes

[hushed sorrel]

Ok, I understood something different

My bad

[rapid badger]

Ok I’m thoroughly confused, I’m guessing this changes the whole thing since we both thought it was a set format with a tree diagram

[hushed sorrel]

Then yes the answer to the second question would probably not be the same

[rapid badger]

Ok, but does the reasoning of 2/127 stay the same?

[hushed sorrel]

Let's find that out

[hushed sorrel]

The configuration can only be valid if Ken and Ryu are not in the first match together, and they both win, and they are both paired together

You could consider conditional probabilities here I think

P(all of that) = P(R and K are paired together in the second round | they were not paired together in the first round, they both won) × P(they were not paired together in the first round, they both won)

[rapid badger]

I only learned how to calculate given, dependent, independent, and the Union and Intersect thing, conditional probability just means for example event X won’t occur if event Y doesn’t happen right?

[hushed sorrel]

P(A inter B) = P(A | B)P(B)

[rapid badger]

That’s conditional probability?

[hushed sorrel]

A | B is A given B

[rapid badger]

Ah ok I know that

[hushed sorrel]

Here the B one is a bit long

But you can try step by step

[rapid badger]

Ok

[rapid badger]

Ok, I got 1/252

Which is 2 digits less for the denominator (assumed answer is 1/254)

[hushed sorrel]

How did you do it? To verify your method

[rapid badger]

What I did:

1/4 x 126/127 x (1/63 / 126/127)

[hushed sorrel]

Yeah I did the sam

[rapid badger]

I used this as a reference for what I should do

[rapid badger]

Oh, at least that was the same TwT

Thanks for the help, perhaps I’ll revisit this another day. I’ve been stuck on it for 2 hours (while doing other questions but still)

[hushed sorrel]

It looks good to me

[rapid badger]

Oh, maybe we can just continue assuming that it’s right then

[hushed sorrel]

Note that the reasoning in the key is wrong

For the reason you specified

The second round matchups are independent of the first one's so there is no notion of adjacent match

[rapid badger]

Ah shoot

So where did the 2/127 come from?

[hushed sorrel]

Well if the tournament structure was tree-like it would be consistent with the given argument

[rapid badger]

Or is it wrong since the answer sheet is pretty suspicious anyways

[hushed sorrel]

But since we established it was not the case

[rapid badger]

I c

[hushed sorrel]

Then the argument given in the key is incorrect

We just find the same results by chance

[rapid badger]

So what graph would you recommend to make to help solve?

Or do you just kinda have to know P(B) and all that stuff to make an equation for the answer

[hushed sorrel]

You don't need a graph, just specify the event you want to compute the probability of

And rewrite it using conditioning

Specify what is A, what is B, what is A|B

And compute their probability, apply the formula

[rapid badger]

Do you think there are simpler questions I can try practicing on online before I come back to this?

This is the extra/extension question so I would like to try working up to it

[hushed sorrel]

No clue, I am not a specialist on online resources

[rapid badger]

I c, ty for all the help then

Do threads auto delete?

[hushed sorrel]

You are welcome buddy

[rapid badger]

Ideally I’d like to keep this as reference to try again tmr

[hushed sorrel]

They are not deleted

[rapid badger]

Oh jackpot!

[hushed sorrel]

Just keep a link to this post

And you can close it

[rapid badger]

Nice, tysm again!! Huge help

[hushed sorrel]

And come back to view it

As long as you have the link

[rapid badger]

I c

[hushed sorrel]

https://discord.com/channels/624314920158232616/1313825816421072946

Here is the link

[rapid badger]

Ty

+close

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