What is the maximum gain after two coin tosses for a person who starts with $1 if the occurrence of a head produces a 50% gain while the occurrence of a tail produces a 50% loss?
A) $1.00
B) $1.25
C) $1.75
D) $2.25

Question

Quizplus · Accepted Answer

After the first coin toss, there are two possible outcomes:
- Head: the person's money increases by 50%, so they end up with $1.50.
- Tail: the person's money decreases by 50%, so they end up with $0.50.
After the second coin toss, there are four possible outcomes:
- Head then head: the person's money increases by an additional 50%, so they end up with $2.25.
- Head then tail: the person's money increases by 50% and then decreases by 50%, so they end up with their original $1.00.
- Tail then head: the person's money decreases by 50% and then increases by 50%, so they end up with $1.50.
- Tail then tail: the person's money decreases by an additional 50%, so they end up with $0.25.
The maximum gain is $2.25, which occurs when the first two coin tosses are both heads.

What Is the Maximum Gain After Two Coin Tosses for a Person