I need some clarification on a topic which has caused a debate between my family - though it is only me on one side...
Essentially, given a lottery with a 1 in 70000000 chance of winning a jackpot with one ticket. There is a disagreement that if you have 2 tickets your odds of winning is now not approximately (1 / 35000000). I've attempted to explain that if you bought 2 tickets that the first tickets probability of winning is 1 in 70000000 and the second ticket's chance is also 1 in 70000000. Surely this is the case as if you bought 35000000 tickets you would have a 50% chance of winning. However, they seem to think that the chance increases far too rapidly. Additionally, they have been misinformed by Google saying that if there is 100 tickets in a lottery and you buy 2 tickets then you have a 1 in 99 chance of winning as 1 has to be a loser which is ludicrously incorrect in my mind because that would mean that if you bought 50 tickets then you would have a 1 in 49 chance... Someone help me settle this. Please!
You are indeed correct. Let's visualize the problem as the following:
Suppose we had a small lottery with three tickets. Obviously, with 1 ticket, the probability of winning is $\frac13$. Now let's think about the case we had two tickets. Let's assume that our friend John has the other ticket. We know that his probability of winning is $\frac13$, and either he wins the lottery, or you do. So, your probability of winning the lottery is $\frac23$.
This idea can be generalized to large lotteries, but this small example helps to develop intuition.