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In a Bernoulli trial, the likelihood of the number of successive failures before a success is obtained is represented by a geometric distribution, which is a sort of discrete probability distribution.

We are given, $75\%or0.75$of millennials who have a profile on a social networking site and in order to find a person without a profile on a social networking site is$(1-0.75=0.25)$.

Make the list of values that you want the X may take on where an upper bound for the situation can be seen at hand so,

$X~G(0.25)$

The mean in geometric distribution is $mean=\frac{1}{p}$where $p=0.25$as we are to find the person without a profile on a social networking site

$$\begin{gathered} mean=\frac{1}{p} \\ mean=\frac{1}{0.25} \\ mean=4 \end{gathered}$$

Standard deviation is $\sqrt{\frac{1-p}{p^2}}$where $p=0.25$

$$\begin{gathered} 未=\sqrt{\frac{1-p}{p^2}} \\ 未=\sqrt{\frac{1-0.25}{{(0.25)}^2}} \\ 未=3.4641 \end{gathered}$$

The probability that ten people find one person without a social networking site is calculated as follow:

$$\begin{gathered} P(X=10)={(1-0.25)}^{x-1}脳(0.25) \\ P(X=10)={(0.75)}^9(0.25) \\ P(X=10)=0.0188 \end{gathered}$$

The probability that $20$people find one person without a social networking site is calculated as follow:

role="math" localid="1649166303751" $$\begin{gathered} P(X=20)={(1-0.25)}^{x-1}(0.25) \\ P(X=20)={(0.75)}^{19}(0.25) \\ P(X=20)=0.0011 \end{gathered}$$

The probability that at most five people is calculated as follow:

$$\begin{gathered} P(X鈮�5)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5) \\ P(X鈮�5)=0.7627 \end{gathered}$$