Hey Ayush, I had a doubt. Is there no chance that dear Trevor goes on and on in opposite direction? Then the probability would be close to 1 but not equal to?
Yes, there should be a case where Trevor keeps on walking in the opposite direction on and on. But this would be just one case in an almost infinite number of possible paths.
The set of possible paths (even infinite paths included) would be countable. Considering the frequentist principle of probability, an event's probability is the limit of its frequency while performing the trials. If you consider it as a fraction, that is:
P(he does not die) = lim (n->inf) [(choosing that 1 path)/(all n possible paths)]
This would be zero and would match with the idea above.
Infinity is a very interesting concept; consider the unit interval [0,1]. What is the probability of picking up the value 0.5. If you think of it, it is the same question as above, and the answer is 0. (Here, I am slightly abusing the concept of continuous PDFs and countable sets)
gg work <3
Nice one ! Would be an even better experience if equations are nicely formatted with LaTeX.
By equations I mean the expressions in between the actual text .
Noted! We tried out Latex initially, but it was not supported nicely. We'll definitely find a way around by this week's post or next.
Hey Ayush, I had a doubt. Is there no chance that dear Trevor goes on and on in opposite direction? Then the probability would be close to 1 but not equal to?
Yes, there should be a case where Trevor keeps on walking in the opposite direction on and on. But this would be just one case in an almost infinite number of possible paths.
The set of possible paths (even infinite paths included) would be countable. Considering the frequentist principle of probability, an event's probability is the limit of its frequency while performing the trials. If you consider it as a fraction, that is:
P(he does not die) = lim (n->inf) [(choosing that 1 path)/(all n possible paths)]
This would be zero and would match with the idea above.
Infinity is a very interesting concept; consider the unit interval [0,1]. What is the probability of picking up the value 0.5. If you think of it, it is the same question as above, and the answer is 0. (Here, I am slightly abusing the concept of continuous PDFs and countable sets)