Could there be a typo in part (i) of this question?
But the result gives P(T=2)=pq(2-q-qq). Or I’m being an idiot. Either way, put me out of my misery.
Pinned this to see if anyone else has insight!
I think that P(X=2\cap Y=1)=qp\times p should give you an answer that agrees with their formula.
Hope this helps.
So I just assumed the question was A wants a head and B wants a tail…oops.
Here’s my stab at a solution, including the most welcome difference of two squares…
Q12 STEP3 2020.pdf (2.1 MB)