Question

A fair coin is tossed. If the first coin lands heads, you win 1$ and the game stops. If you first toss tails, you lose 2$, but you get to toss one more time. If it lands heads you lose 1$, but if it lands tails, you win 5$. Use the tree diagram to determine the fair value of this game.
http://media.apexlearning.com/Images/200908/26/eb3540b9-fd2c-4c6d-b7be-7680b7c43143.jpg

A. $0.50
B. $0.25
C. -$1
D. $1

Wouldn't it be D since -3+4=1? Just double checking my thinking...

Answer 1

Or would it be A? since you only have a 50% chance each time and so you cut each $ amount in half, then ad the negative to the positive and get 0.50

Answer 2

lets take all the cases
1) It lands head first time probability of this event = 1/2
2) it lands tail first time and then again tail = 1/2*1/2
3) it lands tail first time and then head = 1/2*1/2
so fair value
1*0.5+(-3)*5.5*0.5 + (3)*0.5*0.5

Answer 3

that equals -7

Answer 4

sorry second value is 0.5 not 5.5

Answer 5

made a typo :(
did you understand how I formed the equation?

Answer 6

yeah I do, thank you!

Answer 7

np :)