Hi,

Im currently studying 12th grade advanced mathematics and have come across this rather difficult probability question. It has three parts. I'm struggling in particular with parts ii) and iii). Could somebody please provide worked solutions as i unfortunately do not have answers to this problem. Any help will be much appreciated.

Question:

There are 4 red discs and 3 black discs in bag. Sophie and Emma play a game where they each have a turn at drawing a disc with replacement. Sophie starts.

Sophie wins when she draws a red disc and Emma wins when she draws a black disc.

(i) What's the probability that Sophie wins on the first draw?

(ii) What is the probability that Sophie wins in the first 3 draws. (either 3 or less)

(iii) What is the probability that Sophie wins the game

Appreciate any help