Social networking sites for business professionals are used to promote$$ one's business. Each social network involves interactions$($connections$)$ between members of the network. Researchers define network density as the ratio of actual network connections to the number of possible$$ one$-$to$-$one connections. For$$ example, a network with $10$ members has left parenthesis Start $2$ By $1$ Matrix $1$st Row $1$st Column $102$nd Row $1$st Column $2$ EndMatrix right parenthesis

equals$45$ total possible connections. If that network has only $5$ connections, the network density is StartFraction $5$ Over $45$ EndFraction

equals$\mathrm{.}111.$ Sociologists at the University of Michigan assumed that the density x of a social network would follow a uniform distribution between $0$ and $1($Social Networks,$2010).$ Complete parts a through c below.