 # To explain the pros and cons of binomial probability tables. Jerold 2021-10-02 Answered
To explain the pros and cons of binomial probability tables.

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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.