Kate and James are playing a game. They are taking it in turns to pick counters out of a bag. There are 8 green and 6 yellow counters. They don’t put the counters back in the bag after they have been picked.
Kate picks first, and she picks a green counter. Then, James goes, and he also picks a green counter. Lastly, Kate picks again, and she picks a yellow counter. Find the probability of this happening in its simplest form. Then, find the probability for the same problem in the case that they put the counters back in the bag. Report your answer in the simplest form for both when they don’t put the counters back in the bag, and when they do put the counters back respectively.