Question

You are given 3 to 1 odds against tossing three tails with three​ coins, meaning you win ​$3 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. Find the expected value​ (to you) for the game.

Answer 1

Step-by-step explanation:

• 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
• $Probability(x)=P(x)\\P(0)=\frac{1}{8} \\P(1)=\frac{3}{8} \\P(2)=\frac{3}{8} \\P(3)=\frac{1}{8}$
• 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