Question

1) What does the expression "n independent trials" mean?

2) If you carry out an experiment of repeatedly rolling a die and recording the results. Would that be considered a binomial distribution experiment?

3) What's the difference between combination and permutation?

Answer 1

1. n independent trials means that you are conducting the experiment in such a way that no trial depend on each other.

That is outcome of a trial does not depend on any other trial.

2. Consider an experiment where you throw a die for n times and record the number of six appeared in the uppermost face.

Here ,

a) The trials are independent since throws of a dice at a specific trial do not depend on other trial

b) Trials can be divided into two parts success and failure. That is if six appears it is a success, otherwise failure.

c) Probability of success remains same from trial to trial i.e. 1/6

Hence we have a sequence of Bernoulli trials. So, it is a binomial experiment.

3. Permutation is how many arrangements you can have where order is important.

Combination is how many arrangements you can have where order is not important

A, B and C are three objects,

then permutations will be, [ ABC , ACB, BCA, BAC, CAB, CBA ]

Combinations will be , [ABC] beacuse all will be considered as same since order is not important here.