4D Results for Draw date: Wed 27/06/07
First Prize: 6904
Second Prize: 6904
Third Prize: 7173
Starter Prizes:
0453 1910 3578 4147 5253
5545 6595 8027 8102 8808
Consolation Prizes:
0500 1298 1530 2199 3142
3206 3216 3875 7595 7760
Wednesday, June 27, 2007
4D Results for Draw: 2560
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1 comments:
Same 4D number as first and second prizes: Probability is actually just one in 10,000
A LETTER of mine entitled '4-D fallacy' was published in the electronic forum of this paper sometime in November last year.
In that letter, I corrected the error of stating that the probability of a number to be selected for both the second and third prize in the 4-D lottery was one in a hundred million.
At the end of the letter, I wrote: 'A similar miscalculation regarding the probability of a number winning the first prize in two different draws was reported some years ago. Tongue in cheek, what is the probability of such an error occurring twice?'
It seems from the report, '1 in 100m chance: 6904 wins top two prizes in 4-D draw' in the June 28 edition of The Straits Times, that the probability of such an error will be one if there is no need for all concerned to brush up on their numerical literacy.
In our society today, the ability to understand numbers and their stories, and the logical-mathematical capacity to follow and critique a quantitative argument is, to say the least, very important for understanding the world and for decision making.
Should we buy 4-D tickets? Are we in a hot streak? What about the property market? The media especially, with its huge reach and influence, should ensure fidelity in numbers reported and their mathematical interpretation.
I reproduce below the mathematical argument of my first letter with relevant adjustments for the new situation.
The probability is actually just one in 10,000. The calculation is as follows.
List all the outcomes for the first and second prize numbers to be the same. They are 0000-0000, 0001-0001, 0002-0002... 9999-9999, making a total of 10,000 favourable outcomes. The total number of outcomes would be 10,000 � 10,000 since there are 10,000 possibilities for the first prize winner and 10,000 possibilities for the second prize winner. The probability of a number to be selected for both the first and second prize is the number of favourable outcomes divided by the total number of possible outcomes, that is, 10,000/(10,000 � 10,000) = 1/10,000.
To obtain the probability as one in a hundred million (much more sensational than one in ten thousand), one has to fix the winning number. That is, the probability that 6904 (and 6904 alone) wins both the first and second prize is calculated this way.
List all the outcomes for the first and second prize numbers to be 6904. They are 6904-6904, making a total of one favourable outcome. The total number of outcomes would be 10,000 � 10,000 since there are 10,000 possibilities for the first prize winner and 10,000 possibilities for the second prize winner. The probability of 6904 to be selected for both the first and second prize is the number of favourable outcomes divided by the total number of possible outcomes, that is, 1/(10,000 � 10,000) = 1/100,000,000.
In fact the occurrence of at a number winning at least two prizes out of the 23 prizes is 1 - 0.9999 � 0.9998 � 0.9997 � ... � 0.9978 = 0.025, that is, about one in 40, not so unusual at all.
At the rate of three draws a week, this event will occur about once every three months - sometimes two consolation prizes, sometimes first and starter, sometimes second and third, and so on.
Dr Tay Eng Guan
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