Actually. There's a math behind this.
Dice for example. The probability of rolling a 6 is 1/6. If you're rolling 2 of them, the probabolity that both will be 6 is not 1/12, more of 1/36.
Probability is determined by Events/Number of outcomes. Probability of multiples is determined by multiplying all the events together.
Going back to dice, you have 2 events each with a 1/6 chance of hitting 6. 1/6 x 1/6 = 1/36
If you still dont believe me, take a look at how many ways you can combine numbers on 2 d6:
1-1
1-2
1-3
1-4
1-5
1-6
2-1
2-2
2-3
2-4
2-5
2-6
3-1
3-2
3-3
3-4
3-5
3-6
4-1
4-2
4-3
4-4
4-5
4-6
5-1
5-2
5-3
5-4
5-5
5-6
6-1
6-2
6-3
6-4
6-5
6-6
As you can see, there are 36 unique combinations you can make. Didn't think I'd actually use this shit I learned in high school.
So. Going back to your lottery. If you have 1 ticket for each lottery, it doesnt matter whether you got the tickets in the same lottory or a different lottery. You have 2 chances of 1/10,000,000 winning. So your chances are actually 1/5,000,000 at winning either or lottery.
NOW. If you're gonna get greedy and you want to win both lotteries, your chances of winning both A and B lottery are 1/100,000,000,000,000
Good luck