Nothing and Some More

Hello world... again! Am I Ugly in Grey, or what ??

pop.ul.ar

Looking for the The Google Font? It is Catull, but found out more about the Google logo by reading the Google Font Page

Fancy reading my Looking for the Spam collection ? It's even getting multilingual

Linux, Linux, Linux, Linux... want to try it ??? Knoppix is really nice. And easy. Download, burn, reboot. Et voila, Linux is running...

The Probability of Random Death in an Election Compared to Winning the California Super Lotto - 08/02/2002

I propose to you a game of chance. If you accept, read below.

On the occasion of both the Commune Elections in Cambodia and an unusually big Super Lotto Jackpot here in California this week, I was thinking about how one would compute the probability that 23 candidates and activists only from FUNCINPEC and SRP could randomly "die". Let me say from the outset that I do not intend this exercise to make light of what's happened--but instead to use statistics to show how very unlikely it was for these events to have been completely "random". Let me also add that I do not belong to any party.

I don't think I have enough information to compute the exact probability, but let me think through the problem. I would need the total number of candidates from each of the three parties, which is likely the number of communes times three (let's ignore extraneous parties for now). The key assumption would be that each "event" (i.e., death) is statistically independent from any other event. This feature makes it "random".
Imagine an urn filled with balls of three colors: Green (FUNCINPEC), Blue (SRP), and Red (CPP). Now, draw from the urn with (or is it without?) replacement 23 balls. When a candidate or activist is killed, a new candidate or activist from that party is inserted in his/her stead (in this sense, there is replacement... even though, technically, it's not the same person--and it can never be the same person... may all the merits s/he made bring them happiness and considerably more safety in their next life).
The question then is: How likely is it that given the proportion of balls in the urn (for each color), ONLY Green and Blue balls are drawn after 23 draws? Again, each draw is an independent event with replacement (thus very much like a Simple Random Sample, SRS, with its attendant assumptions of the the central limit theorem and normality of distribution--for a wonderful interactive simulation see: http://www.bera.com/dieframe.htm).

Assuming that FUNCINPEC, SRP, and CPP all had candidates and activists in every commune, the urn would be filled with 1/3 Green, 1/3 Blue, and 1/3 Red balls. Every draw, each color has a 1/3 chance of being selected. For Green or Blue, the probability is 2/3 chance (the sum of each). What then is the probability that after 23 seperate draws not one single Red ball is drawn? Is it 2/3^23? That would be 0.000089 or about 0.0089% chance of this event occuring. This is equivalent to odds of 1 in 11,222 (and I am rounding down). My knowledge of urn statistics is rusty, I apologize, so correct me if I am wrong.

Here are the odds of winning the California Super Lottery (straight from the website http://www.calottery.com/games/superlottoplus/howtoplay.asp):

Instructions: Pick five numbers from 1 to 47 and a MEGA number from 1 to 27 on the playslip (I've even attached an image of the payslip! Quick, jot them down on a piece of paper since you decided to read on and play this game of chance!)

All 5 of 5 And Mega: 1 in 41,416,353
All 5 of 5: 1 in 1,592,937
Any 4 of 5 and Mega: 1 in 197,221
Any 4 of 5: 1 in 7,585
Any 3 of 5 And Mega: 1 in 4,810
Any 3 of 5: 1 in 185
Any 2 of 5 And Mega: 1 in 361
Any 1 of 5 And Mega: 1 in 74
None of 5 Only Mega: 1 in 49
Overall odds of winning: 1 in 23

Based on my "rough" back of the envelope (or is it back of the e-mail) calculations above, the likelihood that 23 candidates and activists of SRP and FUNCINPEC would die completely randomly is greater than getting any four out of five numbers on the California Super Lotto. Close, but no cigar to the jackpot, I realize. In California, this would not make you a millionaire (the current prize for getting all 5 of 5 and the mega correct is $63 million as of the February 6th Jackpot), but it would still make you an extremely lucky man or woman (and a fistful of dollars richer if I am not mistaken). In Cambodia, these unlikely odds over the last few weeks would have made you a certifiably dead man or woman (candidate or activist, but remember, only from either SRP or FUNCINPEC!).

Sophal

P.S. If you had played California's Fantasy 5 game instead, you would have won between $199 and $801, but quite possibly a whole lot more.
All 5 of 5 winning numbers 1 in 575,757 Pari-mutuel** $18,179 to $531,360
Any 4 of 5 winning numbers 1 in 3,387 Pari-mutuel** $199 to $801
Any 3 of 5 winning numbers 1 in 103 Pari-mutuel** $11 to $21
Any 2 of 5 winning numbers 1 in 10 Free Replay
Overall odds of winning 1 in 9

P.P.S. For the record, the California Super Lotto Draw #1549 on 2/6/2002 was 36, 3, 46, 32, 42, and the Mega was 24.

P.P.P.S. Would you like to play again?

(via Camnews, © Sophal Ear)
Originally published as jemisa.editthispage.com/discuss/msgReader$361
08 février 2002