Question

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 theywill make you play a game. Your sister says she wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $3 times the number thatthe spinner lands on. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $9 if the spinner lands on blue and $21 ifthe spinner lands on red. Determine the expected value of each game and decide which offer you should take.AnswerKeypadKeyboard ShortcutsExpected value for your sister's game:Expected value for your mother's game: SWhich offer should you take?your sister's offeryour mother's offer

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

expected value of each game = ?

Step 02:

Expected value:

Sister:

total outcomes = 6

1 - 6

probability = 1/6

1 | 2 | 3 | 4 | 5 | 6

$3 | $3 | $3 | $3 | $3 | $3

1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6

`\text{expected value = \$3}\cdot(1)/(6)+\text{ \$3}\cdot(1)/(6)+\text{ \$3 }\cdot\text{ }(1)/(6)\text{ + \$3}\cdot(1)/(6)+\text{ \$3}\cdot(1)/(6)\text{ + \$3 }\cdot\text{ }(1)/(6)`

expected value (sister) = $3

Mother:

total outcomes = 2

blue - red

probability = 1/2

blue | red

$9 | $21

1/2 | 1/2

`\text{expected value = \$9 }\cdot\text{ }(1)/(2)\text{ + \$21}\cdot(1)/(2)`

expected value (mother) = $15

The answer is:

Expected value (sister) = $3

Expected value (mother) = $15

Mother's offer.