2015 Query (1 Viewer)

[DatAtarLyfe]

So the q. 14 c) (iii) in the 2015 paper is


Pretty simple and I worked it out. But I looked at their answers:

And their first line of working out stops at the playing winning 2n games, when I pretty sure you have to include the probability 2n+1 games as well. Am I right or is there am I missing something?

I mean they're numerical answer and everything preceding is correct, but it was just their initial statement

 

[DatAtarLyfe]

Anyone...

 

[InteGrand]

So the q. 14 c) (iii) in the 2015 paper is
View attachment 33518

Pretty simple and I worked it out. But I looked at their answers:
View attachment 33519
And their first line of working out stops at the playing winning 2n games, when I pretty sure you have to include the probability 2n+1 games as well. Am I right or is there am I missing something?

I mean they're numerical answer and everything preceding is correct, but it was just their initial statement

The answers actually did up to 2n+1 games, they just wrote to go up to 2n games by accident I think. The last term in their series in the first line was (2n choose n)*(1/2^{2n+1}). This is indeed the probability that A wins in 2n+1 games, because we fix the last game as an A win, then we choose n more A wins from the first 2n games, hence the (2n choose n). (The 1/(2^{2n+1}) is fairly self-explanatory.)

 

[DatAtarLyfe]

The answers actually did up to 2n+1 games, they just wrote to go up to 2n games by accident I think. The last term in their series in the first line was (2n choose n)*(1/2^{2n+1}). This is indeed the probability that A wins in 2n+1 games, because we fix the last game as an A win, then we choose n more A wins from the first 2n games, hence the (2n choose n). (The 1/(2^{2n+1}) is fairly self-explanatory.)

Cool, yeah i know they put up to 2n+1 games in their working, was just confused why they stopped at 2n in their statement

 

[InteGrand]

Cool, yeah i know they put up to 2n+1 games in their working, was just confused why they stopped at 2n in their statement

Ah. Yeah that was probably just a typo/blunder (the sample solutions have some disclaimer at the start saying that they may not be complete or even correct, if I recall correctly).