Probability and Statistics Part 2
2 min readMay 4, 2020
Independent Events
If two events are independent, the probability of one does not change if the other occurs. Mathematically,
However since above equation is not valid if P(B) = 0, we use a symmetric definition:
For multiple events,
Independent Trials
Binary Trials
Also called Bernoulli trials, it is a sequence of identical independent experiments such as repeated coin tossing. Given the probability of one event (p), the probability of the other event is 1 — p. The probability of a particular sequence of N trials with the k occurrences of the event with the probability p is:
Non-binary Trials
A set of outcomes for m-ary experiment is:
It has respective probabilities:
A particular sequence has respective occurrences of:
The probability of such sequence is:
