AR. My I 7/14 Question 9 of 14, Step 1 of 1 You need to borrow money for gas, so

Question

AR. My I 7/14 Question 9 of 14, Step 1 of 1 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 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. Your mother says she wants you to flip a fair coin. She will give you $8 for heads and $32 for tails. Determine the expected value of each game and decide which offer you should take. Keypad Expected value for your sisters game: S Expected value for your mother's game:S Which offer should you take? your mothers offer

Explanation / Answer

Sister's game:

probability each event occuring in spinner = 1/6 since it is fair spinner and has six out comes.

If spinner lands 1, payout = $6

Similarly spinner 2 = $12

spinner 3 = $18

Spinner 4 = $24

Spinner 5 = $30

Spinner 6 =$36

Multiplying all the respectie probablities with the payout or each event = 1/6(6+12+18+24+30+36)

= 1+2+3+4+5+6

= $21

Expected value of Sister's game = $21

Mom's game:

Probability of heads or tails in a fair coin is 1/2

Payout for heads = $8

Payout for Tails = $32

Expected value = 1/2(8+32)

= 4 + 16

= $20

Expected value of mom's game is $20.

Offer provided by sister shoud be taken since it has a higher expected value.

Also, by other logic, only when 1 lands on the spinner we get a payout of $6, all other numbers on spinner will give higher payout than mother's lowest payout of $8. Hence sister's offer should be taken.

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