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Sagot :
Answer:
$-0.60
Explanation:
Given that:
Cost of playing game = $3 per game
Number of ducks = 10 (each duck is numbered from 1-10)
If you pick the duck numbered 10, you win $15
If you pick any of the ducks numbered 7, 8 or 9, you win $3
If you pick any other duck, you win nothing
The expected value of the game is given by:
[tex]\begin{gathered} Probability=\frac{chance}{Possible\text{ outcome}} \\ P(duck_{10})=\frac{1}{10}=0.1 \\ P(duck_{7,8,9})=\frac{3}{10}=0.3 \\ P(duck_{others})=\frac{6}{10}=0.6 \\ Game\text{ }Cost=\text{\$}3 \\ \text{The expected value is given by:} \\ E(X)=Probility\text{ }of\text{ }winning-Game\text{ }Cost \\ E(X)=15(0.1)+3(0.3)+0(0.6)-3 \\ E(X)=1.5+0.9+0-3 \\ E(X)=2.4-3=-0.6 \\ E(X)=\text{\$}-0.60 \end{gathered}[/tex]Therefore, the answer is the fourth option ($-0.60)
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