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

y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x y

0 0

1 -3

3 -9

-2 6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

Answer from: Quest

answer: do we write it

step-by-step explanation:

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