That is incorrect.
The probability will always be % \(50\) because each turn, there is a 50-50 chance that the coin will be heads or tails.
Please post this as an Off-Topic post, not a math question.
It didn't have any guts. Ha, ha.
Ok, I just wanted to make sure!
Did you mean to add a slash here? 1/((1 - a)(1 - ab)) + 1/2*a/((1 - a)(1 - ab)) + 1/2*b\(/\)((1 - a)(1 - ab)) = (a + b + 2)/(2(1 - a)(1 - ab))