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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 lose 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

Respuesta :

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:

[tex]E(X)=\sum {X\times P(X)}[/tex]

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

[tex]E(X)=\sum {X\times P(X)}[/tex]

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

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.