A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Please I need some intelligence,Patience...To help me in solving this question.Ty.
anonymous
 4 years ago
Please I need some intelligence,Patience...To help me in solving this question.Ty.

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0An ant stands in the middle of a circle (3 metres in diameter) and walks in a straight line at a random angle from 0 to 360 degrees. Problem is, it can only walk one metre before it needs a break. The ant has the memory of a fish and forgets what direction it has just walked in.. Anyway, after the break, it gets all dizzy and thus chooses another random direction from 0 to 360 in an attempt to escape the circle again. As you can well imagine, it could escape the circle after just 2 walks (just one break needed). Or... it could take 20,000 walks (19,999 breaks needed)!! There might even be the very slim possibility it might take 20,000^20,000 walks.... What is the average amount of walks required for the ant to escape the circle?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@satellite73 ,@Calcmathlete

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0there is no snap solution to this problem i think try googling it and you will come up with many many posts, since apparently this is a common problem no good solutions though

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0am I on the completely wrong track to say that since he has a remaining 0.5 to go to escape the circle that \(\cos\theta\ge\frac12\implies\frac\pi6\le\theta\le\frac\pi6\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0not completely wrong....ur on the right track...:)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0I mean \[\frac\pi3\le\theta\le\frac\pi3\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes...now u just compute the average

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u do realize the ant neednt exactly go by ur condition!!

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0so that is 1/3 of a circle... so there is a 1/3 chance he gets out on move 2 where do I include the average, I still don't quite get it :/

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0true...good enough. avearge is when u consider a particular no. of test cases. so if u consider 100, there is 33% chance of getting out on the 2nd move. now all u have to do is calculate the remaining chances for the other angles he might take....now although this is quite random, the probability for each angle range decreases n goes like a geometric series

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0yeah that's where the problem for me is... a geometric series is a good idea if we can set one up, but since the exact angle that he returns on is variable that won't be easy

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0like he could godw:1341369002782:dw(move 1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yup...its a tedious problem...but i think a general solution is difficult but not impossible to obtain.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1341369028085:dwthat leaves him with a 0% chance of leaving the circle in the next move, ordw:1341369061211:dwin which case he has some other odds of leaving the circle in the next move

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0@Zarkon probability problem, interested?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0for all u know, there is even the possiblity like the question itself that the ant might not come out at all if he keeps taking angles that put him back inside.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0that was suggested by @Outkast3r09 on an earlier post, but @Eyad says there is a definite answer, so...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://math.stackexchange.com/questions/133851/antinacircle. this page has a good solution.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0well that still is not as elegant as I was hoping where's the actual answer now...?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.011.4 is the "expected value" so I guess that's the answer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok Then Ty everyone :) Ty @TuringTest ,@amrit110 :ty for the site its useful :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.