I am pretty sure my mathematics correct and it is so simple but there is something bugging me like I’m missing something.
Suppose the expectation of an event E(x) = n. Now we add some variables. The first variable increases the probability of the event p(x) by 25%. The second variable decreases the probability of the event by 7%. What is the new E(x)?
You also want to be clear about what is meant by “increase the probability by 25%”. Does that mean adding 25 percentage points to the probability (e.g., 40% to 65%), or does it mean multiplying the probability by 1.25 (e.g., 40% to 50%)? I’ve seen it used both ways, in different contexts. If possible, ask your source to clarify.
This is different than your original question. This question has one factor that affects probability and another factor that affects value. So they would multiplied together as you show here.
But your OP asks about two factors that both affect probability. If they are independent then you should consider them separately:
E(x) = n x (0.25 - 0.07)
For example, if the probability of getting a heart attack if I am 50 is 0.08 and the chance of being hit by lightning if I live in Virginia is 0.001, then if I am a 50-year-old living in Virginia the chance of either having a heart attack or being hit by lightning is 0.081, the sum of the probabilities.
It is not clear from the formulation of your original question what calculation should be applied.
Except buying another ticket doesn’t double your chances, either, since your chance also depends on the total number of tickets sold. In fact, your expectation in a 50-50 raffle is directly proportional to the number of tickets you buy.