If there are 75 tickets and one 1st prize the chance is 1/75 x 100 in percentage terms. If the number of tickets doubles to 150 but there are now two 1st prizes (first 2 tickets drawn) do the odds of winning a 1st prize increase, decrease or stay the same?
I think the maths is 1/150 x 100 = 0.66666 recurring Plus 1/149 x 100 = 0.67114 = 1.33781 Compared with 1/75 x 100 = 0.33333 recurring.
So yes better odds. Do I have my maths right?
The probability of winning in the first setting is $\frac{1}{75}$, that is true.
As I understand the game, you cannot win both prices in the second setting. The probability of having the first ticket that is drawn is $$p(\text{first ticket}) = \frac{1}{150}$$ The probability of being the person with the second ticket drawn is $$p(\text{second ticket}) = \frac{149}{150} \cdot \frac{1}{149} = \frac{1}{150}$$ because you must be one of the 149 persons not having the first ticket and the one person winning when the second ticket is drawn.
Putting it together you have a probability $$ \frac{1}{150} + \frac{1}{150} = \frac{1}{75}$$ so your chances stay the same.
You could also think of it like this: The probability of not winning is $$p(\text{neither the first nor the second ticket}) = \frac{149}{150} \cdot \frac{148}{149} $$ so the probability of winning becomes $$ 1 - \frac{149}{150} \cdot \frac{148}{149} = 1 - \frac{74}{75} = \frac{1}{75}. $$