/ High Stakes Gambling Odds

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Moggsy on 01 Mar 2013
Any mathematicians out there.....

The 6 number lotto win is ~1:14million.

What are the odds of naming 6 random numbers then, these coming out as a bonus ball within a 6 month period, 2 draws per week?

Jack B on 01 Mar 2013
In reply to Moggsy:

6 months is 26 weeks, or 52 draws.
There are 49 balls, unless I'm mistaken, and each draw includes one bonus ball. All draws are unrelated. I'm going to assume all 6 random numbers are different and the order doesn't matter - because I assume that's the case for a valid ticket? I don't do lottery tickets.

The probability that your first number never appears is (48/49)^52
The probability that your first number did show at some point then is is (1-(48/49)^52)
Given that your first number has shown up, the probability you never see your second is (48/49)^51. Similarly the probability you do is (1-(48/49)^51).
The probability you see both is then (1-(48/49)^52)*(1-(48/49)^51).

You can see then that the probability of getting all six is:

Product from n=47 to 52 of (1-(48/49)^n)

Which is about 1 in 15 .

No doubt someone with a better grasp of probability will be along shortly to point out the errors in my maths...
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foxwood on 01 Mar 2013
In reply to Moggsy:

I think you will find the odds are enormous number since you require each of your 6 named numbers to appear specifically as the 7th ball drawn !

Hopefully someone who understands the calculus better than me will give you the exact answer.

If you want to see how likely certain numbers are to win have a look at this simulator which you can leave running with your pet numbers http://justwebware.com/uklotto/uklotto.html

Buying one ticket a week you can expect to win the top prize once in approximately 250,000 years - buy 6 a week and it will only take 45,000 years.

Mind you, if you bought £100 of tickets each week then you would almost certainly win £10 about once every week (odds of 57:1)

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