I want to win with Probability!!!
You are about to play a game with a coin that is weighted so that there is a 90% chance that it lands heads and a 10% chance that it lands tails. If you want to maximize the expected amount of money you will win, would you rather...
A. win $10 if it lands heads,
B. win $50 if it lands tails, or
C. win $1,000,000 if it spontaneously combusts in the air. (You may assume that there is at most a 0.0000001% chance that the coin will spontaneously combust in the air.)
Choose wisely!
Assuming I win nothing when I lose a game the following will be my expected value of this discrete Bernoulli random variables
and assuming I only have one try.
for option A the E(x) = 0.910 + 00.1 = $9
for option c the E(x) = 500.1 + 00.9 = $5
for option C it is the chances of spontaneously combusts or not spontaneously combusts thus it it's Expected value is: 0.0000000011000000 + 99.9999...0 = $0,001
thus by pure expected value I would choose option A because it has the highest expected value. But lets say I can play any amount of games I want, then I will also choose option A for it has a stable and high chance of growth!.
so final answer overall, option A!