Parmi | #1 draft pick | Jake King is **** | Big Bash League tipping champion of the universeCome and Paint Turtle
LOL, you're right.
Greatest Ever Test XI: JB Hobbs, L Hutton, DG Bradman (c), IVA Richards, BC Lara, GS Sobers, AC Gilchrist (wk), Imran Khan, RJ Hadlee, MD Marshall, SK Warne 12th man: M Muralitharan
Favorite XI: WG Grace, VT Trumper, IVA Richards, DCS Compton, FMM Worrell (c), AC Gilchrist (wk), CL Cairns, SK Warne, FS Trueman, SE Bond, T Richardson 12th man: H Larwood
"Neither of them will have an international cricket career past 2016."
Blocky on Martin Guptill and Ish Sodhi. 20/11/2014.
"Cricket is an art. Like all arts it has a technical foundation. To enjoy it does not require technical knowledge, but analysis that is not technically based is mere impressionism."
- C.L.R. James
Hulululu has 3/4th chance of dying and 1/4th chance of breaking into 2 Hulululus. If broken into 2, each of these 2 Hulululus have the same chances - 3/4th chance of dying and 1/4th chance of breaking into 2 further Hulululus....and so on.
What's the probability that the Hulululu species will never be extinct?
I'm massively sleep deprived but: 0. Monkeys, Shakespeare, etc.
Yeah the sum you'd set up would converge to 1, wouldn't it?
**** I hate probability. Prefer something nice and clean like finding two irrationals a and b such that a^b is rational.
do you think people will be allowed to make violins?
who's going to make the violins?
My immediate reaction was to keep it simple and go with tree diagrams, but the splitting in two part threw me off.
Immediately I thought it was (1/4)^n with n becoming very large, but obviously that doesn't work.
Secondarily I thought in terms of series; the probability being quartered each step as there are two, but I doubt that holds up mathematically. That would have been 1/4 * 1/16 * 1/64 ...
So whatever the formula is [I got P(n)=1/(4^n), but I may be very wrong], as n becomes very large you approach zero, so it is almost certain they will become extinct at some point.
Last edited by Dan; 27-12-2012 at 06:34 AM.
Repeating patterns, mate.
OK. Assume 'if we start with a bacteria, the probability of the species finally going extinct is p'. Then,
p = 3/4 + 1/4*p*p
=> (p-2)^2 = 1
=> p = 1 [Rejecting the other solution as that can't be a probability number]
So, the probability of of the Hulululu species never going extinct = 1-p = 0
Last edited by weldone; 27-12-2012 at 07:00 AM.
In fact, for any x where 0<x<1, if you replace 3/4 by x and 1/4 by (1-x) in the original problem, then also p will come out as 1 from the equation I think. I'm also sleep-deprived, so not putting an effort to solve that generic one lol.
Alternatively you can look at the expected population at every year.
E(0) = 1
E(1) = 0.5
E(2) = 0.25
E(3) = 0.125
MSN Messenger: minardineil2000 at hotmail dot com | AAAS Chairman
CricketWeb Black | CricketWeb XI Captain
ClarkeWatch: We're Watching Rikki - Are You?
Up The Grecians - Exeter City FC
Completing the Square: My Cricket Web Blog
Also love the fact that he wasn't completely correct.
There are currently 1 users browsing this thread. (0 members and 1 guests)