How do you add percentages of 2 (or more) different situations

Eg:

There is a raffle with 10 tickets, you buy 1 ticket, you have a 10% chance of winning

If there is another raffle with the same odds (you have a 10% chance to win)

What is the chance that you will win at least 1 if not both of the raffles?


Thanks in advance

Your chance of winning the first raffle is 10%.
Your chance of winning the second raffle is 10%.
Your chance of winning at least one raffle is 19%.

You can't simply add the two probabilities, because if you win the first raffle, there's a chance that you will also win the second, and vice-versa. So you have to add the two probabilities, and then subtract the probability that you will win both (because that probability would be double-counted otherwise.)

So, it's 10% + 10% - (10% * 10%), which is 0.1 + 0.1 - (0.1 * 0.1), or 0.20 - 0.01, or 0.19, which is 19%.

Asked another way, what's the probability that you will win neither raffle? If you have a 10% chance of winning, you have a 90% chance of losing, and the chance of losing both is the product of the chances of losing each one, so it's 90% * 90%, which is 0.9 * 0.9, or 0.81, which is 81%. And if your chances of losing both is 81%, then your chances of winning at least one is 100% - 81%, or 19%.

From the question, the probability that you win is 10% if you buy one
therefore, the probability that you win two will be 20% if you buy two
this is the same as that that you win at least one or both

Your chance is 10 % of winning one or the other.
But if you had two ticket in the same raffle you would have a 20 % chance.in that raffle.