The probability of these numbers coming out on lottery ?

Question

Can someone settle an argument. My friend tells me that the chance of any number coming out on Lottery is 49-1 which I agree however he says that this means the odds and probability of any six random numbers are the same odds of numbers 1,2,3,4,5 and 6 coming out . I dont agree but dont know enough about statistical probabilities to prove him wrong.

Answer 1

I do not know enough really either, but would hazard a guess that it is putting an added dimension to the odds.
Normally the odds are for each individual number, now you are adding that an overall pattern must apply as well.

Answer 2

Point 1:The chances of any named number coming out in the lottery are NOT 49-1 nor 1 in 49, as there are SIX numbers drawn, which makes the probability 6/49. Point 2: Any six numbers have the same chance of winning first prize as any other six numbers. There are 49 balls in the lottery in 7 drop columns of 7, not 50 as in an answer elsewhere. For any further information see my answer to the resolved question "What is the probability of a lottery win?"

Answer 3

Point 1:The chances of any named number coming out in the lottery are NOT 49-1 nor 1 in 49, as there are SIX numbers drawn, which makes the probability 6/49. Point 2: Any six numbers have the same chance of winning first prize as any other six numbers. There are 49 balls in the lottery in 7 drop columns of 7, not 50 as in an answer below. For any further information see my answer to the resolved question "What is the percentage chance of a lottery win?"

Answer 4

OK, firstly I am assuming you refer to a 50 ball lottery such as the original UK lottery. This makes a big difference to the answer.

In this instance, assuming all balls are equally weighted and there is no reason for any ball to be preferred to the others, then your friend is correct.

Any ball regardless of its number has an equal chance of being selected as any other on any draw. Sequence makes absolutely no difference as each is a random draw.

1,2,3,4,5,6 is in itself a random sequence in terms of a lottery draw, it just makes sense to us as it is an order we are used to seeing in every day life.

At first glance, the sequence 13, 20, 42, 14, 23, 18 may seem random to you, but it is not.

I selected those as they (before the weekend fixtures at least) represent the Engalnd rugby teams score in their last 6 internationals.

For either of these sequences, the same rules apply. A crude lottery machine is equally unable to affect the selection of the sequence 1,2,3,4,5,6 as it is that of the rugby scores.

So, on to the process itself.

In the first draw this probability is one in fifty, or 1/50 in terms of statistics, or 49-1 in boookmakers odds, the second, 1/49 (as one ball has already been selected in the first draw, and therefore removed from the potential pool for the second), the third 1/48...etc up until the sixth ball at a probability of 1/45

Given you have six numbers selected this makes your chances of successfully having one of your numbers selected on the first draw 6/50. Given that one of your numbers comes up in the first draw, this gives you a 5/49 chance on the second draw, again accounting for one ball removed from the pool.

Repeated success means the probability of success on the third draw is 4/48, then 3/47, then 2/46, then 1/45.

As each of these are independent draws, the overall probablility is the probability of each out come multiplied.

So 6/50 x 5/49 x 4/48 x 3/47 x 2/46 x 1/45

Which give odds of 1/ 15,890,700 or put in simple words one in almost 16 million!

Given that only half the stake money goes on the prizes, my advice to you would be "Don't do the lottery!"

I hope this helps, and didnt bore you too much....

Answer 5

You're right that each digit out of 49 has a 1-49 chance of winning. And the odd for a set of six out of 49, all having a 1-49 chance is exactly 13,983,816 to 1. Six consecutive numbers have never won. The probability is based on what has happened before or not. What has never happened is highly improbable and vice versa. In all lottery games some kind of mixed combination is what usually wins. It's rarely numbers from one group (ones tens twenties etc) let alone numbers from one group in a consecutive pattern. Look at your game history or the history of other games and see if you find 1-2-3-4-5-6 before your eyes get tired. I read a book that said "Lottery officials and mathmaticians like to say that every number and every set of six numbers has an equal chance of winning." But if they both have an equal chance of winning why is it that ramdon sets have always won while sets of numbers numerical order have never won? If you have a 50/50 chance of something happening, such as rain, when there's a 50/50 chance for rain it's never always one or the other. So the chance is not equal.

Answer 6

The odds of 12345&6 are as equal as
any other six digits. Look at any of
the past winning number & you'll see
that none of them have ever repeated.
As well as that 3 odds + 3 evens Seem to
have a better chance, but only because this
combination is greater.

Answer 7

Although he is absolutely correct, any 6 numbers have exactly the same chance as any other.
You asked for statistical evidence to prove him wrong. Statistically you can tell him that to date there has never been a complete sequence of numbers 123456 which have won the top prize, but every prize has been won by numbers not in that numerical sequence. This proves that statistically the chances of getting those number to come up is very very unlikely.

However it is exactly the same chance for any selection of 6 numbers.

Answer 8

1-14 million for each six figure combination.
Once, last year here in germany, we had 1,2,3,4,5 and 24 come up. I been playing on and off for 30 years and the most I got right is 4, about four times, which proves something.....

Answer 9

the odds of 1,2,3,4,5&6 being drawn in the lottery are exactly the same as any other six random numbers being drawn.

Answer 10

No the odds are different because now it's six numbers in a row, not random.