/sci/ - Science & Math

[Anonymous No.3276095]

I was watching the 2002 movie Scooby-Doo. There was a scene that (for me) brought up a question about probability. The scene was as follows:

> We have the four main characters on-screen.
> Within the bodies of those characters are four "spirits".
> Of that set of spirits, one belongs to each character, but is not initially within the body of the character it belongs to.
> Randomly, all the spirits will exit the characters, shuffle around and enter a random character such that each character has a spirit within his or her body once the shuffle is complete.

Questions:
> What is the probability that after a shuffle has occured, all the spirits will be in the correct body?
> How many shuffles is it most likely to take before all spirits are within the correct body?

[Anonymous No.3276104]

>implying anon isn't immediately thinking about being Velma and shlycking-off.

[Anonymous No.3276107]

>I was watching the 2002 movie Scooby-Doo

[Inurdaes !V1sPhobos. No.3276108]

>>3276104
>implying Anon isn't thinking of Scooby instead

>>3276095
Forgive me, but err, it IS sort of a kids movie. And you started thinking of probability?

[Anonymous No.3276109]

>>3276104
>Not sure which one Velma is
I'd feel more comfortable about thinking of either them fingering themselves if the movie was good. It wasn't.

[Anonymous No.3276112]

My job is so fucking unbelievable. I'll try to sum it up by first telling you about the folks I work with:

First, there is this supermodel wanna-be chick. Yeah, okay, she is pretty hot, but damn is she completely useless. The girl is constantly fixing her hair or putting on makeup. She is extremely self-centered and has never once considered the needs or wants of anyone but herself. She is as dumb as a box of rocks, and I still find it surprising that she has enough brain power to continue to breath.

The next chick is completely the opposite. She might even be one of the smartest people on the planet. Her career opportunities are endless, and yet she is here with us. She is a zero on a scale of 1 to 10. I'm not sure she even showers, much less shaves her "womanly" parts. I think she might be a lesbian, because every time we drive by the hardware store, she moans like a cat in heat.

But the jewel of the crowd has got to be the fucking stoner. And this guy is more than just your average pothead. In fact, he is baked before he comes to work, during work, and I'm sure after work. He probably hasn't been sober anytime in the last ten years, and he's only 22. He dresses like a beatnik throwback from the 1960's, and to make things worse, he brings his big fucking dog to work. Every fucking day I have to look at this huge Great Dane walk around half-stoned from the second-hand smoke. Hell, sometimes I even think it's trying to talk with its constant bellowing. Also, both of them are constantly hungry, requiring multiple stops to McDonalds and Burger King, every single fucking day.

Anyway, I drive these fucktards around in my van and we solve mysteries and shit.

[Anonymous No.3276117]

>>3276108
>kids movie
>be 14 years old
herpafuckin'derp tripfag

[Anonymous No.3276121]

Actually There is an episode from futurama that also has this in it. At the end of the episode someone solves the problem with a math theory.

Now that math theory is real and is included in the episode as an easter egg. It's a new theory that was devloped by a hobby mathematision working for futurama. Go watch episode. problems solved

[Inurdaes !V1sPhobos. No.3276122]

>>3276117
Make a coherent point, or do I have to rub my figurative nuts all over your and other haters faces again?

[Anonymous No.3276124]

>>3276112

[Anonymous No.3276129]

>>3276122
wanting to rub his genitalia on other men.

>implying you arent gay

[Inurdaes !V1sPhobos. No.3276133]

>>3276129
>implying you're a man

[Anonymous No.3276139]

>>3276112

>Velma
>0 of 10

I hearby revoke your nerd privileges. Please turn in your brain and glasses at the reception.

[Inurdaes !V1sPhobos. No.3276145]

>>3276139
Don't get too worked up over it, it's copypasta.

[Anonymous No.3276157]

Is anyone actually going to answer the questions?

>in b4 'no'

[Anonymous No.3276169]

can the spirit re-enter the same body it left from?

[Anonymous No.3276180]

>>3276139
requesting moar velma pr0n

[Anonymous No.3276184]

>>3276169
Yes.

[Bruised !crow0v0ifw No.3276211]

<span class="math"> n! [/spoiler] permutations of <span class="math"> n [/spoiler] spirits.
If there is a equal chance to move from permutation to another then <span class="math"> \frac{1}{n!} [/spoiler] to change to identity permutation.

Therefore <span class="math"> \frac{n!}{2} [/spoiler] changes must happen before it is likely before they return.

(Just replace <span class="math"> n [/spoiler] with <span class="math"> 4 [/spoiler])

[Anonymous No.3278673]

>>3276211
E[X] is 1/p for geometric distribution. Since the shuffle is random, p=1/n!, so E[X]=1/(1/n!)=n!, not n!/2.

[Anonymous No.3278685]

>>3278673
Whoa, just realised that OP asked how many shuffles it is most likely to take, not for the expectation.

It's just 1, OP. Because the probability that it happens on the first shuffle is p=1/n!. The probability that it happens on the second is (1-p)*p, on the third is (1-p)^2 * p, and so forth. Since 0<p<1, the probabilty that it happens in later shuffles decreases.

[Anonymous No.3278698]

Of course, the more entertaining question is "what is the probability that NONE of the spirits end up in the correct body?"
And that is a tricky quandary sometimes known as the hat problem.

[Anonymous No.3278716]

>>3278698
Ooh, derangements.

I didn't know it was called that.

[Anonymous No.3278718]

> What is the probability that after a shuffle has occured, all the spirits will be in the correct body?
1/24
>> How many shuffles is it most likely to take before all spirits are within the correct body?
after 17 shuffles, chances are they will have found the right body.

[Anonymous No.3278759]

>>3278698
interesting...
3/8