Discrete examples are easy enough. Toss a coin, 1/2, toss a die, 1/6.

Continuous examples, Probability of a nucleus decaying during observation, 1-exp(-λt), Probability of a neutron moves x without interaction, exp(-Σx), where Σ can be assumed to be the inverse of the mean free path i.e. the distance a neutron travels without interaction on average.

My point is that I don't really have an idea as to how these continuous probabilities are derived. Any assistance?

15 minutes ago, random_soldier1337 said:

My point is that I don't really have an idea as to how these continuous probabilities are derived. Any assistance?

What does the probability tell you?

Why is the probability of getting heads in a coin flip one half and what does that mean?

Once you have this clear you can move on to probabilities of continuous distributions.

Edited October 6, 20187 yr by studiot

Well in the case of the coin it tells me that there are 2 random events that can happen when I flip a coin. The chance that one or the other takes place is 1/2 under the assumption both sides are affected by the same unbiased factors.

Now, taking for example the probability of a nucleus decaying, I know that the number of nuclei in a sample N = N_oexp(-λt), where N_o is the initial amount. Looking at the probability of a nucleus decaying another way, I could put it as 1-N/N_o. I'm not really sure I understand. 1- the percentage of nuclei remaining at a given time gives me the probability?

EDIT: Or do you mean to say that they are derived by observation and large sample sizes of a phenomenon?

Edited October 6, 20187 yr by random_soldier1337