Can you spot the error in this news story from Yahoo Odd news ?
by on Monday, March 29th, 2010 | 6 Comments
A Nebraska Lottery official says the winning numbers for the state’s Pick 3 lottery on Tuesday were exactly the same as the winning combination from the night before.
Lottery spokesman Brian Rockey says one of two lottery computers that randomly generate combinations picked the numbers 1, 9 and 6 — in that order — for Monday night’s drawing. He says the other computer picked the same three numbers Tuesday in the same sequence.
The odds of such an occurrence? One in a million.
In this game, three numbers are picked, each one being a digit 0-9. Repeats are allowed.
And for some bets the order is significant.
The situation described is that the same three numbers, in the same order, were drawn twice in a row.
The game is played 6 days per week.
the lotto doesnt occur 2 days in a row
One in a thousand.
Well, assuming the numbers are picked out of 52, the odds are actually 1 / 132600. That’s almost 10 times less than one in a million.
(1/52)(1/51)(1/50)
One in a million is a wild exaggeration. It’s actually about 1/700 (10!/(10-3)!=720).
Edit: You should have pointed to the lotto info web site (http://www.nelottery.com/pick3.xsp), otherwise it’s not clear if there’s like 10 balls and you choose 3 or if you choose 3 digits independent of each other. I assumed that once a number is chosen, it’s no longer available.
So it is actually 1/10^3=1/1000.
1/10*1/10*1/10 = 1 in 1 thousand for a day.
and to repeat the next day One in a million?
also maybe the numbers are picked my a person. The computer just pops up the ball by air-force, at least in some states.
For the purposes of my answer, let’s assume non-repeating of drawn numbers and that order doesn’t matter giving us
1/(3/10 * 2/9 * 1/8) = 120
Odds of 120:1 against you for any given drawing. Given that a quick look at the Nebraska lottery webpage seems to indicate that numbers can be repeated and that order does matter for the rules of their contest, the odds are going to be stacked even further against you, at 720:1.
Anyway, the point of my answer is that the odds (120:1 or 720:1 or 1000:1 or whatever they are) on the second night were *exactly the same as the night before and don’t change as each drawing is independent of each other.*
Is that the error you were looking for?
Update: I still maintain that the odds of picking 1, 9, and 6 were, 720:1 and that immediately after the first drawing of 1, 9, and 6 that the odds were still one in 720 that they’d be 1, 9, and 6 for the next drawing.
That said, perhaps you’re wanting to treat the two simultaneous drawings as one event, as the reporter did when saying the odds were a million to one in which case I think the odds would be 518400:1, or about “one in half-a-million.”