Question

$\mathit{n}\mathbf{=}\mathbf{50}\mathbf{,}\mathit{p}\mathbf{=}\mathbf{4}\mathbf{/}\mathbf{5}\mathbf{.}$

Short answer

Binomial distribution, i.e., $f\left(x\right)=C(50,x){\left(\frac{4}{5}\right)}^x{\left(\frac{1}{5}\right)}^{50-x}$ .

The graph is shown below

Step-by-step solution

Given Information.

$\begin{array}{rcl}n& =& 50\\ p& =& \left(\frac{4}{5}\right)\\ q& =& \left(\frac{1}{5}\right)\\ & & \end{array}$

Definition of Binomial distribution. 

The discrete probability distribution of the number of successes in a sequence of$\mathit{n}$ independent experiments is the binomial distribution with parameters $\mathit{n}$and$\mathit{p}$ .

Solve binomial distribution for given values.

Binomial distribution is,

$f\left(x\right)=C(n,x)p^x{q}^{n-x}$

Substitute values,

$f\left(x\right)=C(50,x){\left(\frac{4}{5}\right)}^x{\left(\frac{1}{5}\right)}^{50-x}$

Hence, binomial distribution is $f\left(x\right)=C(50,x){\left(\frac{4}{5}\right)}^x{\left(\frac{1}{5}\right)}^{50-x}$.