Question

What are the conditions needed in a binomial experiment? Give some examples of binomial probabilities.

Answer 1

there needs to be only 2 possible outcomes and there also needs to be repeated trials.

e.g rolling a bias die where the probability of rolling a 6 is p = 1/3.

If the die is rolled 4 times what is the probability of no '6's appearing

so not 6 q = 2/3

using binomial expansion of (p + q)^4 = p^4 + p^3q + p^2q^2 + pq^3 + q^4


the answer is (2/3)^4 = 16/81

in general its just