Lost Internet sites often vanish or move, so that references to them can’t be followed. In fact, $13\%$of Internet sites referenced in major scientific journals are lost within two years after publication.$19$If a paper contains seven Internet references, what is the probability that at least one of them doesn’t work two years later? Follow the four-step process.

Within two years of publication, $13\%$ of the internet sites cited in major scientific publications vanish.

Multiplication rule: $P(A\cap B)=P\left(A\right)\times P\left(B\right)$

Complement rule: $P(notA)=1-P\left(A\right)$

$P\left(lost\right)=13\%=0.013$

Complement rule:

$P(notA)=1-P\left(A\right)$

Calculate the likelihood of a reference not being lost within two years using the complement rule.$P(notlost)=1-P\left(lost\right)=1-0.13=0.87$

Multiplication rule:$P(A\cap B)=P\left(A\right)\times P\left(B\right)$

To find the likelihood of not losing within $7$references, use the multiplication rule:

$P(7notlost)={(P(notlost\left)\right)}^7={(0.87)}^7\approx 0.3773$

To calculate the probability of getting at least one losing within two years, use the complement rule:

$$\begin{gathered} P(atleastonelost)=1-P(7notlost) \\ P(atleastonelost)=1-0.3773 \\ P(atleastonelost)=0.6227 \\ P(atleastonelost)=62.27\% \end{gathered}$$