[BNM] [OT] Lottery puzzle

[Alex Farran]

On Mon, Sep 22, 2008 at 5:46 PM, David Pashley <david at davidpashley.com> wrote:
> On Sep 22, 2008 at 17:36, James Cline praised the llamas by saying:
>> If you bought all for the same draw
>>
>> You would have a 52 in 14000000
>>
>
> 52/14,000,000
>
>
>> If you bought each week you would have
>>
>> 1 in 1400000 each time.
>>
>
> 52 * 1/14,000,000 or 52/14,000,000
>

On the face of it it looks that way, but I don't think it's right.
Imagine that instead of 52 tickets you could buy 14,000,000.  Assuming
they're all different numbers you would be guaranteed to win. If
instead you lived long enough to play the lottery every week for 270
thousand years you'd not have the same guarantee.  Though there's a
tiny chance that you'd win every week.

If you scale the numbers down so each ticket has a 1 in 100 chance of
winning you can start to see the difference.

The chance of winning with your 52 tickets is 52/100.

The chance of losing if you play for 52 weeks is (99/100)^52.

Therefore the chance of winning is 1 - (99/100)^52

If you work that out it's a probability of 0.52 for 52 at once vs
0.407 for 1 every week.

BTW I've never played the lottery.  The question was posed to me by my
brother who works in an investment bank.  Make of that what you will!

-- 
Alex Farran Web Development
http://www.alexfarran.com 01273 474065