Question

A game has an expected value to you of $200. It costs $200 to play, but if you win, you receive $100,000 (including your $200 bet ) for a net gain of $99,800.  what is the probability of winning?

Answer 1

The probability of winning the game is calculated by solving the expected value equation for the winning probability, which results in approximately 0.2% chance of winning.

Step-by-step explanation:

The question involves using the concept of expected value to calculate the probability of winning a game. Firstly, we need to recognize that the expected value of playing the game, given as $200, is a result of the weighted average of all possible outcomes. In this case, there are only two outcomes: winning the game with a reward of $100,000 (which includes the return of the initial $200 bet) with the probability we want to calculate, let's call it P(winning), and losing the game, which costs $200 to play with the probability of 1 - P(winning).

Accordingly, the expected value (EV) formula, which is EV = (P(winning) x Win Amount) + ((1 - P(winning)) x Loss Amount), can be represented as $200 = (P(winning) x $99,800) - ((1 - P(winning)) x $200). We can solve this equation for P(winning) to find the probability of winning the game.

After solving, we find that P(winning) = 0.002002. This indicates that the probability of winning the game is approximately 0.2%.