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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.

Respuesta :

SageRage

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
  • [tex]Probability(x)=P(x)\\P(0)=\frac{1}{8} \\P(1)=\frac{3}{8} \\P(2)=\frac{3}{8} \\P(3)=\frac{1}{8}[/tex]
  • The E(x)=Summation (x times P(x))
  • [tex]E(X)=(0)(0.125)+(1)(0.375)+(2)(0.375)+(3)(0.125)=1.5[/tex]
  • 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
fichoh

The expected value is the value of winning made on a game when played overtime. Hence, the expected value of the game is -$0.5 ; with the player losing -$0.5 in the long run.

A coin toss :

  • {H, T}

Sample space for 3 tosses :

  • {HHH, HHT, HHT, HTT, HHT, HTT, HTT, TTT}

Toss required to win = 3 tails :

  • Amount won on success = $3

  • Amount lost otherwise = $1 = - $1

Creating a discrete probability table :

  • X _____ 3 _______ - 1
  • P(X) ___ 1/8 _____ 7/8

The expected probability can be defined as :

  • E(X) = ΣX×P(X)

E(X) = 3 × (1/8) + (-1) × 7/8

E(X) = 3/8 - 7/8 = - 4/8 = -1/2

Therefore, the expected value of the game = - 0.5 ; meaning that, I'll lose 0.5 in the long run.

Learn more :https://brainly.com/question/18405415

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