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Sagot :
Given that:
- Your sister will give you $15 for heads and $25 for tails.
- Your mother will give you $6 times the number that the spinner lands on.
you must calculate the Expected Value of each game:
- Game 1:
When you through the coin, the probability of getting a head is 50% and the probability of getting a tail is 50%.
You need to use the following formula for calculating the Expected Value:
[tex]E=\sum_^x\cdot p(x)[/tex]Where "x" is the random variable, and p(x) is the probability obtained.
Therefore, for Game is:
[tex]E_1=(15)(0.5)+(25)(0.5)[/tex][tex]E_1=20[/tex]- Game 2:
When you spin the spinner with six different outcomes. Therefore:
[tex]p(x)=\frac{1}{6}[/tex]Then:
[tex]\begin{gathered} E_2=\frac{1}{6}\cdot6(1+2+3+4+5+6) \\ \\ E_2=1+2+3+4+5+6 \\ \\ E_2=21 \end{gathered}[/tex]Hence, the answer is:
- Expected Value of your sister's game:
[tex]\text{ \$}20[/tex]- Expected Value of your mother's game:
[tex]\text{ \$}21[/tex]- You should take your mother's offer, because it has the greatest Expected Value.
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