The following excerpt is from an article in The New York Times in July $1999.$While statistics are not available for web entrepreneurs who fail, the venture capitalists that finance such Internet start$-$up companies have a rule of thumb. For every $10$ ventures that receive financingand there are plenty that do not$2$ will be stock market successes, which means spectacular profits for early investors; $3$ will be sold to other concerns, which translates into more modest profits; and the rest will fail.$($a$)$What is a sample space for the scenario?S $=\{2,3,$ the rest$\}$S $=\{$Stock market success, Sold to other concerns, Fail$\}$ S $=\{$Web entrepreneurs, Venture capitalists, Internet start$-$up companies$\}$S $=\{$Web entrepreneurs, Venture capitalists, Ventures$\}$S $=\{10,2,3\}$Correct: Your answer is correct.Good job.$($b$)$Write down the associated probability distribution.Outcomefirst entry of Ssecond entry of Sthird entry of SProbability$0\mathrm{.}2$ Correct: Your answer is correct. Fantastic job!$0\mathrm{.}3$ Correct: Your answer is correct. Nice job$\mathrm{.}0\mathrm{.}5$ Correct: Your answer is correct. Fantastic job!$($c$)$What is the probability that a start$-$up venture that receives financing will realize profits for early investors?