Question

You are given to odds against tossing three with three​ coins, meaning you win ​$4 if you succeed and you lose ​$ 1

Answer 1

To find the E(X) expected value, you come up with the different probabilities for each outcome

your set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tails

Each element has a probability of 1/8 so let x represent number of tails

Probability (x) = P (x)

P (0) = 1/8

P (1) = 3/8

P (2) = 3/8

P (3) = 1/8

The E(x)=Summation (x times P(x))

E ( X ) = (0) (0.125) + (1) (0.375) + (2) (0.375) + 3 (0.125) = 1.5

Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tails

So you can expect to lose money in 1 game

But as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 games