Binomial question maths

Hi, please could i have help on where I have gone wrong on this question? I have attached my working below but apparently, it should be 0.15^r instead, not sure why though?
Thank you.

I think this is ii) and it looks like you have 3/17 at the end rather than 17/3 which would be due to the 0.15 and 0.85 being reversed in the binomial expansion/distribution.
Youre told at the start of the question part that T_r has 0.15^r and T_(r+1) has 0.15^(r+1) so that pretty much defines it? Youve done it the other way round. Arguably the binomial should have been written as (0.85 + 0.15)^50 to reduce confusion, but T_0 would be always on time, T_1 one day late, ... and that is pretty much what youd expect.
Note, not seen the ms, but for 3 marks Id be tempted to almost write down that the T ratio is
0.85 50Cr / (0.15 50C(r+1))
and then simplify or else do this simple simplification right at the start. Your working seems a lot for 3 marks and its harder to see mistakes.

Ohhh ok I didn’t t realise, when you said it should be written as (0.85 + 0.15)^50, why is that?

It can obviously be written either way as p+q is the same as q+p, but the order of the terms / their interpretation is flipped. Here you have
(0.85+0.15)^50
or
(p(on time) + p(late))^50
and the zeroth term p^50(on time) and first term 50 p^49(on time) p(late) and ...
so the 0.15, p(late), is an increasing power as you move along the terms to the right so T_r -> T_{r+1}
Tbh, even though theyve defined it in the question, Im a bit surprised they wrote it as (0.15+0.85)^50 rather than (0.85+0.15)^50. Its an easy error to make in an exam and almost seems deliberately misleading. I guess it should be "lesson learnt" for you and think carefully about the order of p+q (or what is p and what is 1-p) in the exam.