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A local carnival has a game that costs $3 per play. To play, you pick a rubber duck floating in a tub of water. There are 10 ducks, and each one is uniquely numberedfrom 1 to 10. If the duck you pick has the number 10, you win $15. If the duck you pick has 7, 8, or 9, then you win $3. If you get anything else, you don't win anything.Compute the expected value of the game. Be sure to include the cost of playing the game in your calculations. Select the correct choice from the options below.$-3.00$2.40$2.00$-0.60$0.00

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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