SOLUTION: Consider this game: In each turn of the game, you flip a coin three times. If you get three heads, you win 7 points. If you get the sequence “head, tail, head,” you win 3 points. I

Algebra ->  Probability-and-statistics -> SOLUTION: Consider this game: In each turn of the game, you flip a coin three times. If you get three heads, you win 7 points. If you get the sequence “head, tail, head,” you win 3 points. I      Log On


   

Question 699923: Consider this game: In each turn of the game, you flip a coin three times. If you get three heads, you win 7 points. If you get the sequence “head, tail, head,” you win 3 points. If you get any other sequence, you receive no points for that turn. What is your expected value per turn for this game?

Answers:
1.25 points
10 points
2.5 points
4 points
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Outcomes  x=Winnings  p=Probability   x·p
-----------------------------------------------
  HHH         7  pts.      1/8        7/8  pts.
  HHT         0  pts.      1/8         0   pts.
  HTH         3  pts.      1/8        3/8  pts.
  HTT         0  pts.      1/8         0   pts. 
  THH         0  pts.      1/8         0   pts. 
  THT         0  pts.      1/8         0   pts.
  TTH         0  pts.      1/8         0   pts.
  TTT         0  pts.      1/8         0   pts.
-----------------------------------------------
                              ∑x·p = 10/8 = 5/4 = 1.25
Edwin