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58 Select the correct answer. Chris is playing a game with his father with a six-sided die. What is the expected value per roll that Chris will get if his father agrees to give him $2 multiplied by every even number rolled and $1 multiplied by every odd number rolled? OA $1.50 B. $4.50 OC $5.50 OD. OE. Reset Next D $10.50 $12.00 L

Sagot :

Solution:

Given:

[tex]\begin{gathered} A\text{ six-sided die} \\ \\ Possible\text{ outcomes}=1,2,3,4,5,6 \\ Number\text{ of possible outcomes}=6 \end{gathered}[/tex]

Even number:

[tex]\begin{gathered} Even\text{ outcomes}=2,4,6 \\ Number\text{ of even outcomes}=3 \\ Probability\text{ of }even,P(even)=\frac{3}{6} \\ P(even)=\frac{1}{2} \end{gathered}[/tex]

Odd number:

[tex]\begin{gathered} Odd\text{ numbers}=1,3,5 \\ Number\text{ of odd numbers}=3 \\ Probability\text{ of odd},P(odd)=\frac{3}{6} \\ P(odd)=\frac{1}{2} \end{gathered}[/tex]

The expected value is gotten by;

[tex]\begin{gathered} E(x)=\Sigma(x\cdot P(x)) \\ \\ Hence, \\ E(x)=2(\frac{1}{2})+1(\frac{1}{2}) \\ E(x)=1+0.5 \\ E(x)=\text{ \$}1.50 \end{gathered}[/tex]

Therefore, the expected value is $1.50

OPTION A is the correct answer.

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