Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[STMO999]

My lad asked me what the chances are of winning the lottery. I said about 14 million to one (I heard that somewhere). He said that, as we do two lines, that must be 7 million to one. Is that correct? Is two in fourteen million the same as one in seven million?

[Marks DTM Calib]

yes

[alunonhisown]

Still 14 million to one, as you are doing seperate numbers on each line.
I think

[Marks DTM Calib]

There are 14million combinations....you have 2 in your hand and hence you have halved it to 7million...assuming your not stupid and have the same numbers on each line 

[STMO999]

There are 14million combinations....you have 2 in your hand and hence you have halved it to 7million...assuming your not stupid and have the same numbers on each line 

That's what I thought.....then I started to think.......I shouldn't think......

[Debs.]

Predicated as:

6 balls
1-49 numbered

The odds become:

1/49 × 1/48 × 1/47 × 1/46 × 1/45 × 1/44 = 1 in 10,068,347,520

[Bumbazor]

No, with another set of numbers it is another 14millionth of a certainty of matching the numbers drawn, and two 14millionths is one 7millionth.
I did all the possible six number draws, my chances of winning would be 1; a certainty (14 million 14millionths is of course 1).

Edit: for 14millionth, read what Debs has just posted instead, but the theory is still the same.

[STMO999]

Predicated as:

6 balls
1-49 numbered

The odds become:

1/49 × 1/48 × 1/47 × 1/46 × 1/45 × 1/44 = 1 in 10,068,347,520

Thanks Debs, but I just won eff all.

[STMO999]

No, with another set of numbers it is another 14millionth of a certainty of matching the numbers drawn, and two 14millionths is one 7millionth.
I did all the possible six number draws, my chances of winning would be 1; a certainty (14 million 14millionths is of course 1).

Edit: for 14millionth, read what Debs has just posted instead, but the theory is still the same.

Yes. That's logical. But, you know when you talk yourself out of things that you know must be true......

[Marks DTM Calib]

If you want to calculate the odds its as follows;

You have 6 numbers and there are 49 balls
 
First ball comes out

You now have 5 numbers and there are 48 balls

Seconds ball comes out

You now have 4 numbers and there are 47 balls

Third ball comes out

You now have 3 numbers and there are 46 balls

Fourth ball comes out

You now have 2 numbers and there are 45 balls

Fifth ball comes out

You now have 1 number and there are 44 balls

Last ball comes out

So the odds are calculated as

(49 x 48 x 47 x 46 x 45 x 44) / (6 x 5 x 4 x 3 x 2 x 1)

Which equals 13,983,816

Simples

[Marks DTM Calib]

Predicated as:

6 balls
1-49 numbered

The odds become:

1/49 × 1/48 × 1/47 × 1/46 × 1/45 × 1/44 = 1 in 10,068,347,520

A little errorette....its:

6/49 × 5/48 × 4/47 × 3/46 × 2/45 × 1/44

Because you have 6 numbers to start 

[STMO999]

Sorry Debs, but.......

The Chances Of Winning The UK National Lottery
•The Jackpot - 6 Numbers (Typical prize: £2 million)
6 numbers are drawn at random from the set of integers between 1 and 49, which means there are 49!/(6!*(49-6)!) combinations of numbers (the draw order doesn't matter). The means that the jackpot chance is 1 in 13,983,816 or approximately 1 in 14 million.

•5 Numbers + Bonus Number (Typical prize: £100,000)
You are still matching 6 numbers from the 1 to 49 set as above, but you can now do it in 6 different ways (by dropping each of the main numbers in turn), therefore the chance is 1 in 13,983,816/6, which works out as 1 in 2,330,636.

•5 Numbers (Typical prize: £1,500)
This is 42 times more likely than getting 5 numbers + the bonus number because, after the first six balls are drawn, there are 43 balls left and you can match 42 of these 43 balls without matching the bonus number. Therefore the chance is 1 in 2,330,636/42, which evaluates to 1 in 55,491.33333.

•4 Numbers (Typical prize: £65)
Firstly, let's take the case of the first 4 of your numbers matching and the last 2 not matching. In this single case (where each set of chances relies on the previous event occurring):
Chance that your 1st number matches a winning number is 1 in 49/6.
Chance that your 2nd number matches a winning number is 1 in 48/5.
Chance that your 3rd number matches a winning number is 1 in 47/4.
Chance that your 4th number matches a winning number is 1 in 46/3.
Chance that your 5th number doesn't match a winning number is 1 in 45/(45-2) [because there are still 2 unmatched winning numbers].
Chance that your 6th number doesn't match a winning number is 1 in 44/(44-2) [yes, still 2 unmatched winning numbers].

Now you need to accumulate all those chances by multiplying them together:
1 in (49/6)*(48/5)*(47/4)*(46/3)*(45/43)*(44/42) which is 1 in 15486.953. Now this is the chance for that single case occurring, but there are 15 combinations of matching 4 from 6 [6!/(4!*(6-4)!)], so you divide the answer by 15 to get 1 in 15486.953/15 or 1 in 1032.4.


•3 Numbers (Constant prize: £10)
Follow exactly the same scheme as the 4 match above to get these figures:
1 in (49/6)*(48/5)*(47/4)*(46/43)*(45/42)*(44/41) (which is 1 in 1133.119) for a single case. There are 20 combinations of 3 from 6 [6!/(3!*(6-3)!], so the chance of a 3 match is 1 in 1133.119/20 or 1 in 56.7.
The chance of you winning any of the above prizes is approximately 54 to 1 - it is reckoned an average of one million people per draw will win a prize.
Using some computer software I wrote, I calculated how many prizes would be won if all combinations of the 13,983,816 tickets were bought:

Category     Prizes        Chances
Jackpot           1    1 in 13,983,816
5+bonus           6    1 in  2,330,636
5-match         252    1 in     55,491.33
4-match      13,545    1 in      1,032.40
3-match     246,820    1 in         56.66
--------------------------------------------------------------------------------Total       260,624    1 in         53.66

[STMO999]

Spot on Mark!!!!!!!!

I hate you

[Marks DTM Calib]

Spot on Mark!!!!!!!!

I hate you

Why thank you kind sir.........

I spend to much of my life using maths!

[Debs.]

Predicated as:

6 balls
1-49 numbered

The odds become:

1/49 × 1/48 × 1/47 × 1/46 × 1/45 × 1/44 = 1 in 10,068,347,520

A little errorette....its:

6/49 × 5/48 × 4/47 × 3/46 × 2/45 × 1/44

Because you have 6 numbers to start 

  That`s Gentlemanly-speak for; you`re wrong!