Question

You are given 2 to 1 odds against tossing three heads with three​ coins, meaning you win ​$2 if you succeed and you lose ​$1 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.

Answer 1

Answer:

- $0.625

Step-by-step explanation:

To win 3 heads must be obtained, the probability of this is:

p = (1/2) ^ 3 = 0.125

Now, let's review the other scenarios:

HHH -> 0.125

HHT

THH ----> p (2H, 1T) = 3 * 0125 = 0.375

HTH

HTT

TTH ----> p (1H, 2T) = 3 * 0125 = 0.375

THT

TTT -> 0.125

So the waiting value would be:

EV = 2 * 0.125 - 1 * 0.375 - 1 * 0.375 - 1 * 0.125

EV = - 0.625

That is to say that the waiting value is - $ 0.625

The outcome og 1 game cannot be predicted but 100 you loss because the expected value is negative