Binomial probability tables eliminate most of the computations required in calculating the probability for binomial distributions case. However, they contain only a relevant small number of different value of trials (n) and success probability (p). For binomial distribution, the probability of getting x number of success in n trails is given by:

\(p_{x}=\left(\begin{array}{c}n\\ x \end{array}\right) p^{x}(1-p)^{n-x}\)

(n)

0 and 1

Where p is the success probability in 1 trail. The binomial probability table have the probabilities calculated for different combinations of n,p and x. But the table does not include all the possible values. For example: For \(\displaystyle{n}={3},{p}={0.227}\ {\quad\text{and}\quad}\ {x}={2}\), the binomial probability table does not have the probability value for this combination. Hence, in this case, the probability of getting 2 successes in 3 trails need to be calculated manually.