To answer the question on the most likely inconsiderate lumber man i would say the chances of the man entering the lane right next to you at that exact time are very low. Since there are 16 lanes and you chose a middle lane, there is a 1/8 chance the man would jump in a lane directly next to you. Usually people want to be further away from strangers so i find it strange that the man chose a lane right by you (this decision is probably a factor in the probability but i don't know how to calculate it). Finally, it takes you 45 seconds to swim 50 meters. During 7 of those seconds you are at the side of the pool where the lumpy man is getting ready to jump. So the probability of the man jumping in the pool while you are at the same side of the pool is 7/45. The answer of your question would be 1/8 x 7/45 = 7/360. This probability would be even less if you factored in that he could have gone to the pool at any time of the day. I think the man was trying to be rude based on this data...
One time my brother and i played a fun game with chips. My brother got out 2 sea salt and vinegar kettle cooked chip and 8 normal kettle cooked chips (the chips look the same). I absolutely loathe vinegar and the game was i had to eat 3 out of the 10 chips. It was a really fun game and i did end up having to eat a vinegar chip along with 2 normal chips. The probability that i would get a vinegar chip would be (8C2 x 2C1)/(10C3)= 7/15 probability
