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Mathematics
24.10.2020 00:05
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Lottery ticket to game a cost five dollars. The 10,000 tickets sold, one wins $10,000,

Lottery ticket to game a cost five dollars. The 10,000 tickets sold, one wins $10,000, five wins $2000, and 20 wins $500. Find the expected value of the winnings for a single ticket.
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amllamas4972
amllamas4972
4,7(62 marks)
\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
J(\stackrel{x_1}{4}~,~\stackrel{y_1}{-15})\qquad 
K(\stackrel{x_2}{x}~,~\stackrel{y_2}{y})
\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{x+4}{2}~~,~~\cfrac{y-15}{2} \right)\implies \stackrel{midpoint}{L(-1,8)}\implies 
\begin{cases}
\cfrac{x+4}{2}=-1\\\\
x+4=-2\\
\boxed{x=-6}\\
------\\
\cfrac{y-15}{2}=8\\\\
y-15=16\\
\boxed{y=21}
\end{cases}

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