Explain this Brilliant.org odds / probability problem to me

[Rosss]

So you can have a look at it below; The thing I don't quite grasp is that if you know that the spot the previous guy landed on wasn't a winner --and you take the next one-- you are effectively taking one of the bad rolls out, aren't you? If you choose to spin again, you have a chance of rolling the same color / number that the guy previous to you just rolled.

 

I don't know, it's just trippy to me and the explanation doesn't cut it in me mind

[Fasauceome]

The explanation comes down to this:

what are the odds that the winning spaces are right next to the space you landed on? as it turns out, quite low.

 

The odds of you spinning and landing on a winning space are 1/3, always. The odds of landing on the one space in the whole circle that's next to the winning spaces (in a clockwise fashion) is only 1/4

[Tamesh16]

yeah, so spinning the wheel, the probability of landing on each colour is 1/6,  so probability of winning by spinning again is 2/6 , 

however the probability of shift is a bit weird, 

so basically i wanted to avoid it, but works by trying to find probability of winning given that you lost on first attempt, but probability of winning by losing then shifting is basically only 1/6 because he must land on the 4th slice , (if winning ones are together)

but losing then spinning , is higher, so landing on losing position is 4/6 and then landing on winning after is 2/6 and two attempts created a probability of 6/36 = 1/6 , so equally likely, but considering the probability after he already lost is 2/6 for spinning and 1/6 for shifting 

[Ratisbona]

I think an easier explanation would be to look a how many possiblilites you have for winning field combinations, knowing that green is not a winning field.

Given the cinstraint that the two winning fields have to be next to each other you have four options:

Winning fields could be blue/purple, purple/red, red/orange or orange/yellow. As you are determined to only be allowed to shift to yellow, you'll have a one in four chance of that being in the winning combination.
Spinning again gives you a two in six or one in three chance, which should hence be the option of choice.

[ATFink]

Just compare the possible winning combinations based on knowns and unknowns.

 

Here are the possible of winning combinations based upon knowing green loses:

Wins on shift to yellow

Loses on shift to yellow

Loses on shift to yellow

Loses on shift to yellow

 

As you can see there are 4 possible winning combinations knowing green doesn't win.

Each scenario above is equally possible. The yellow tile only occupies 1 of these 4 possible winning scenarios, therefore shifting to yellow means there is a 1/4 chance of winning.

 

On the other hand since 2/6 tiles win that means re-spinning has a 1/3 chance of winning. It doesn't matter if the tiles are adjacent or not once respun since the tile that will be landed on is completely random.

 

1/3 chance of winning on re-spin vs 1/4 chance of winning on shift means you are more likely to win on re-spin. You are actually 33.333% more likely to win on re-spin vs shifting to yellow since 1/3 is 33.333% greater than 1/4.

[LukeLinusFanFic]

Just a follow up question about brilliant:

Are there any courses beyond the high school math I've seen in the ads? Any university stuff?

In general, anyone knows a site that can top khan academy?

[Rosss]

10 hours ago, SwagMaestro said:

Just a follow up question about brilliant:

Are there any courses beyond the high school math I've seen in the ads? Any university stuff?

In general, anyone knows a site that can top khan academy?

I believe there is, just go to their website and sign up; it has free courses. I'm trying to relearn algebra/calculus with it. Just started last night though.. I got decent grades in HS because I literally just memorized the steps for every type of problem we'd have. But I have the hardest time conceptualizing math so i'm hoping this helps so I can actually understand what i'm doing lol

[LukeLinusFanFic]

11 hours ago, Rosss said:

I believe there is, just go to their website and sign up; it has free courses. I'm trying to relearn algebra/calculus with it. Just started last night though.. I got decent grades in HS because I literally just memorized the steps for every type of problem we'd have. But I have the hardest time conceptualizing math so i'm hoping this helps so I can actually understand what i'm doing lol

Once you're finished with calculus 1 it gets much easier and less conceptual bs.

I don't know who your lecturer is, but it's important to understand the differential theorems like Lagrange and understand how it communicates with stuff you learned in high school.

 

Eventually you'll realize it's not the end of the world though. Don't let the definition of the limit scare you.