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Zanzabum
3 years ago
12

Bill is playing a game of chance with the following payout. 30% of the time you will lose 20 dollars, 20% of the time you will l

ose 40 dollars. 10% of the time you will win 50 dollars, 40% of the time you will win 5 dollars. Find the expected value of the event and explain if Bill should play this game based on the mathematical expectation.
please helpppop asappppp and show work so I understand please ​


Anybody know this??? please help
Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

The expected value of playing the game is -$7.

Bill should not play this game.

Step-by-step explanation:

The probability distribution of gain and loss is as follows:

  X         P (X)

-$20       0.30

-$40       0.20

$50        0.10

  $5        0.40

Total        1.00

The expected value of a probability distribution is given by:

E(X)=\sum {X\times P(X)}

Compute the expected value of playing the game of chance as follows:

E(X)=\sum {X\times P(X)}

         =(-\$20\times 0.30)+(-\$40\times 0.20)+(\$50\times 0.10)+($5\times 0.40)\\\\=-\$6-\$8+\$5+\$2\\\\=-\$7

The expected value of playing the game is -$7.

The expected value of the game suggests that Bill will incur a loss of $7 if he plays.

So, it is safe not to play the game.

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Answer:

1/ 6

Step-by-step explanation:

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PLEASE HELP ASAP! I don’t recall how to do this!
MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

(1.05)^x=1.885

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

ln(1.05)^x=ln(1.885)

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

x=\frac{ln(1.885)}{ln(1.05)}

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

ln(x*x^2)=5

Simplifying gives you

ln(x^3)=5

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

ln(x)=\frac{5}{3}

Take the inverse ln by raising each side to e:

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(2^2)^x-6(2)^x+8=0

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But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

2^x=4,2^x=2

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

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For the second solution, we will raise the 2 on the right to a power of 1 to get:

2^x=2^1

Now that the bases are the same, we can say that

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