Binomial Distribution

What are the conditions of using the binomial distribution model?

• There are fixed finite number of trials (n).

• There are exactly 2 outcomes of each trial (success or failure).

• The outcome of each trial is independent of the outcome of the other trials.

• The probability of success (p) remains constant.

How is X denoted if it follows a binomial distribution?

If X follows a binomial distribution then it is denoted X ~ B(n, p).

n is the number of trials.

p is the probability of success.

If p is the probability of success, what is the probability of failure?

1-p.

It is sometimes denoted as q.

What is the formula of r successful trials?

P(X=r)= ⁿCᵣpʳqⁿ⁻ʳ

r= 0, 1, 2…n

• n is the number of trials.

• p is the probability of success.

• q is the probability of failure, so that q= 1-p.

• r is the number of successes (out of n).

More than…

P(X>r).

At least…

P (X≥r).

At most / No more than…

P (X≤r).

How do you calculate binomial probabilities using a calculator?

• Press ‘Menu’, then ‘7’.

• Select ‘4’: Binomial PD to get the probabilities of individual values i.e. ‘=’.

• Select ‘1’: Binomial CD to get the probabilities of cumulative values i.e. ‘≤’.