\[P(X=x)={\binom{n}{x}}p^x(1-p)^{n-x}\] \[\binom{n}{x}=\dfrac{n!}{x!(n-x)!}\]
\[P(X{\leq}x_i)=\sum_{i=1}^{n}P(X=x_i)\] \[P(X{\geq}x_i)=1-\sum_{i=1}^{n}P(X=x_{i-1})\] \[P(X{<}x_i)=\sum_{i=1}^{n}P(X=x_{i-1})\] \[P(X{>}x_i)=1-\sum_{i=1}^{n}P(X=x_{i})\]
\[P(x_1<X<x_2)=P(X<x_2)-P(X<x_1)\] \[P(x_1{\leq}X<x_2)=P(X<x_2)-P(X{\leq}x_1)\] \[P(x_1<X{\leq}x_2)=P(X{\leq}x_2)-P(X<x_1)\] \[P(x_1{\leq}X{\leq}x_2)=P(X{\leq}x_2)-P(X{\leq}x_1)\]
\[z=\dfrac{z-\mu}{\sigma}\] \[P(x_1{\leq}X{\leq}x_2)=P(X{\leq}x_2)-P(X{\leq}x_1)\] \[P(X{\geq}x)=1-P(X{\leq}x)\]