Question
A coin is tossed three times. If heads appears on all 3 tosses, Mary will win $16. If heads appears on 2 of the
tosses, she will win $2. The game costs $5 to play. What is her mean expectation?
tosses, she will win $2. The game costs $5 to play. What is her mean expectation?
Answers
MathMate
Assuming Mary gets nothing from the other outcomes.
For 3 tosses,
outcome probability(P) return(E)
HHH 1/8 $16
HHT 1/8 $2
HTH 1/8 $2
THH 1/8 $2
Mean expectation
= Σ PE
= 16/8 + 3*2/8
= 2+6/8
= 2.75
For 3 tosses,
outcome probability(P) return(E)
HHH 1/8 $16
HHT 1/8 $2
HTH 1/8 $2
THH 1/8 $2
Mean expectation
= Σ PE
= 16/8 + 3*2/8
= 2+6/8
= 2.75