Chance Of Lottery Win If Two People Enter

[espookid]

If the odds of winning a lottery are 13million to one but only two people enter what are the chances of one winning

[fiction-factory]

Call them A and B
Do you want chance of JUST ONE winning
Chance of just one = P (A wins) + p (B wins)= near as dammit 2 in 13 million I think

[fiction-factory]

Is that the question you meant to ask though?

[fiction-factory]

It's not as simple as that though since if 13 million people entered although the expected number of winners is 1 there could be no winners or there could be several

[stuey]

The number of tickets sold in a lottery has no bearing at all upon the odds of you winning. If it's a raffle, then yes, the number of tickets sold does.

[dannyk13]

The odds of winning are determined by the lottery numbers not by the number of people entering so surely the odds of one person winning remains the dame at 13 million to one.

[dannyk13]

same^^

[fiction-factory]

Yes. I was assuming espookid knew that and just wanted to know what the chances were of one of the two winning.
But I suppose that as that is never going to happen maybe he has misunderstood how the lottery works.

[fiction-factory]

I don't undertstand why the question asks about two people. Why two rather than one?

[dannyk13]

I presume the OP thought that the odds would be affected by how many people entered

[JJ109]

The answer is 6.5 million to one approx assuming that they are unaware of the numbers each other pick.

If person a has a 13 million to one chance and person b has a 13 million to one chance, then the probability of one winning is 1/13mil 1/13 mil
= 2/ 13 million = 1/6.5 million.

Techniclly in maths terms you have to subtract the probability tht they BOTH win. BUT as this is 1 / (13 million * 13 million) = 1 in 169 trillion, this fctor cn essentially be ignored.

Answer = 1/6.5 million approx

[stuey]

You are assuming that there is going to be a winning ticket: that isn't true. Say the odds are indeed 13 million to one, you could buy 13 million tickets, and your are still not guaranteed a win.

[Calibax]

It's the same as the chance of one person buying two (different) tickets winning: 2 in 13 million (actually nearer 14 million)

[fiction-factory]

I think we are all just saying the same things and now just need espookid to see if we have answered the question he wanted to ask

[JJ109]

No - I am calculating the probbility that ONE person wins if there are only two tickets. If there are only two tickets it is highly unlikely that anyone will win - in fact 6.5 million to one is the probability.

[dannyk13]

If the odds against picking all six numbers are 13 million to one then the odds of each ticket winning is still 13 million to one.

[fiction-factory]

Not sure why you said "no" there JJ109 as your 6.5 million to 1 is to all intents and purposes the same as 2 in 13 milliion

[fiction-factory]

So we all agree

[JJ109]

FF - I agree with you - I was responding to Stuey as I believed he was referring to my answer. This my or may not hve been the case.

[espookid]

The question is the ODDS are indeed 13 million to one for getting the CORRECT numbers but as only two people have entered and I gave no stipulation of a time limit then what is the CHANCE of one winning ,not what are the odds as we all agree on those but the chance .Which I believe to be evens. If thirteen million enter it is thirteen million to one CHANCE and ODDS but if lets say one person alone entered then he alone can win .OK it might take a millennium but the chance is the same

[fiction-factory]

So you want the chance of any one of two people winning at some time in their lifetime. Are you referring to a single weekly draw?