You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $15 for heads and $25 for tails. Your mother says she wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $6 times the number that the spinner lands on. Determine the expected value of each game and decide which offer you should take.

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LuccianoB499856go LuccianoB499856go · Answer 1

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.