Question

Outcome Payout
HHH $10
HHT $3
HTH $0
HTT -$3
TTT $10
THH -$3
THT $0
TTH $0


Kara is playing a game where she flips a coin 3 times. She wins and loses different amounts of money based on the outcomes. What is the EXPECTED VALUE for the game?

Answer 1

Expected value is the sum of the probability of each even times the outcome of the event.

So she wins $10 with probability 2/8, $3 with probability 1/8, $0 with probability 3/8, and loses $3 with probability 2/8.

So,
E = 10(2/8) + 3(1/8) + 0(3/8) - 3(2/8)
=5/4 + 3/8 - 3/4
=7/4 = $1.75

Answer 2

Crap!

Answer 3

here you mean?

Answer 4

I see it...10(2/8) = 10/4

Answer 5

yeah...stupid arithmetic error

Answer 6

each of these has probability
\[\frac{1}{8}\] so just compute
\[10+3-3+10-3\] and divide by 8

Answer 7

i get
\[\frac{17}{8}\] where did the 4 come from?

Answer 8

Ack! Too early. That'll teach me not to stay up so late playing video games.

Answer 9

in a situation like this think of "expected value" as the average. add up and divide by total

Answer 10

Yeah, i should have. But I've conditioned myself to do it the full way since I've had sadistic teachers who throw in unfair coins into the mix.

Answer 11

but these are the only answer choices


A)
$0


B)
$2.13


C)
$3.29


D)
$4.14