Probability question.

Alpha Dog 1

So a question for the geniuses here.
I'm trying to work out odds on a gambling site regarding the lotto.

Can anyone work out odds for 3 selected balls to be drawn from 7,given that lotto balls go from 1-45?
Anyone explain how to do it?

ChemHickey

Alpha Dog 1 wrote: »

So a question for the geniuses here.
I'm trying to work out odds on a gambling site regarding the lotto.

Can anyone work out odds for 3 selected balls to be drawn from 7,given that lotto balls go from 1-45?
Anyone explain how to do it?

So first of all, consider your 7 numbers are "good balls" and the remaining 38 as "bad balls".


So you want 3 of your good balls to be picked from the 7 you have in the game. This means you have 7C3 choices of this happening (read as 7 choose 3)

Then, you must multiply this by the drawing of 4 balls from the 38 bad ones. The reason you multiply is because you need 3 good balls AND 4 bad ones. AND in probability means multiply. The possibilities for this happening is 38C4.

To finish it off, you must divide by the total number of outcomes from choosing 7 balls from the entire vat of 45. This is 45C7.

So the answer would be

[(7C3)(38C4)]/(45C7) which is (35x73815)/45379620 and ~ 0.05693139343

Hope this helps :P

Alpha Dog 1

Would I be right in saying it's 569/1?
Odds wise?

ChemHickey

Alpha Dog 1 wrote: »

Would I be right in saying it's 569/1?
Odds wise?

No, I don't think so.

I'd say 1 in 17.5650013069 chance, as you have ~0.0569 chance of it happening and 1/17.565 ~=0.0569

BeanbagBallbag

I don't think he means he has 7 numbers selected I think he means he has a bet on 3 specific numbers to come out in the draw of 7 numbers from 45.

So say you have for example 1,2&3 as your numbers, then you have

3/45 * 2/44 * 1/43 = 1/14190
multiplied by 7C3 = 7/2838 = 0.002467

So that's roughly 405/1, where the bookies give roughly 300/1 I think.

Hope that helps!

Alpha Dog 1

That's it exactly, they offer 325/1.
Had 2 numbers last night!!

Neil3030

Wow. That's nearly a 25% vig.

I would steer clear of that book.

Alpha Dog 1

BeanbagBallbag wrote: »

I don't think he means he has 7 numbers selected I think he means he has a bet on 3 specific numbers to come out in the draw of 7 numbers from 45.

So say you have for example 1,2&3 as your numbers, then you have

3/45 * 2/44 * 1/43 = 1/14190
multiplied by 7C3 = 7/2838 = 0.002467

So that's roughly 405/1, where the bookies give roughly 300/1 I think.

Hope that helps!

Sorry Ive another question.
So its 405/1 for 3 selected balls to to be drawn from 7, if it was 3 from 6 how would the odds change ?

BeanbagBallbag

In that case it's what I did before, except it would be multiplying by 6C3.

That would give 2/1419 =0.00141 which is roughly 710/1!

Alpha Dog 1

Cheers bean bag balls bag.