Mathematics, 14.11.2020 21:20 Marleneg

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.

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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 - 1P(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.

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Answer from: winchester729

Step-by-step explanation:

To find the E(X) expected value, you come up with the different probabilities for each outcomeyour set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tailsEach 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

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 tailsSo you can expect to lose money in 1 gameBut 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

Answer from: Quest

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

Answer from: Quest

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation:

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