/ 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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