In fact, for any x where 0<x<1, if you replace 3/4 by x and 1/4 by (1-x) in the original problem, then also p will come out as 1 from the equation I think. I'm also sleep-deprived, so not putting an effort to solve that generic one lol.
"I want to raise my hand and say one thing. Those who complain about my love for the game or commitment to the game are clueless. These are the only 2 areas where I give myself 100 out of 100."
- Sachin Tendulkar, as told in an interview published in Bengali newspaper Anandabazar Patrika after his 100th International century (translated by weldone)