PeroK's latest activity

The events must be mutually exclusive but not necessarily independent. Although, in this case, you still need to look at the events in...

There are generally two points of view about trying the impossible. The first is that by setting your sights on an impossible goal, you...

I think what makes such a puzzle such as this one interesting is that it is counting on there being a subtle confusion between...

The main thing I learned in my studies of probability is to try not to see the situation as a process. That's tricky. Strive to come...

That's not a serious proposal, as it misses the whole point. In QM, systems are defined by quantum states, not by the precise, well...

More simply: $$E = \sum_{k=1}^{n}kp(k)$$where ##p(k)## is the probability of precisely ##k## matches in a set of size ##n##. The trick...

I see what you mean.

PS for a mathematical example, see Stirling's formula as an approximation for large factorial...

It might not produce the formula but something numerically almost equivalent. For example, QED produces a formula that is not the same...

You don't have to guess. I've proved it's 1 in each case!

Put 10 balls in a bag, numbered 1-10. The probability that the first ball is #1 must be 1/10. The probability that the last ball is #10...

Sure, it must. For any ##n## you can match any number up to ##n## except ##n-1##. For your example that is zero and two. That doesn’t...

The probability of any number matching is 1/n. Over a large number of trials, k, it will match k/n times. So, the total number of...

Imagine repeating the experiment many times. How often does 1 get matched to the corresponding element from set B? If there are n...

This can be true. Some people won't thrive in academia as a whole for the same reason I wouldn't thrive in pure maths research. There...