Question

You are given 5 to 4 odds against tossing three heads heads with three​ coins, meaning you win ​$5 if you succeed and you lose ​$4 if you fail. Find the expected value​ (to you) of the game. Would you expect to win or lose money in 1​ game? In 100​ games? Explain. Find the expected value​ (to you) for the game.- ​$___ ​(Type an integer or a decimal rounded to the nearest hundredth as​ needed.)

Answer 1

$-2.875 in 1 game

$-287.5 in 100 games

Explanation:

As the probability of getting head in tossing a fair coin is 0.5, the probability of getting 3 heads with 3 coins is 0.5*0.5*0.5 = 0.125

So you have a 0.125 chance of winning and 0.875 chance of losing a game

The expected value for 1 game would be

0.125*5 - 0.875*4 = -2.875

On average you would be losing 2.875 per game. In 100 games you should expect to lose 287.5 dollar