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PLZZZZ HELP!!!
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 lose 40 dollars, 10% of the time you win 50 dollars, 40% of the time you win 5 dollars. Find the expected value of the event and explain if Bill should play this game based on the mathematical expectation.

Respuesta :

Answer:

  • Expected Value= -$7
  • Bill should not play the game

Step-by-step explanation:

In the game, these are the payout:

  • 30% of the time you will lose 20 dollars.
  • 20% of the time you lose 40 dollars.
  • 10% of the time you win 50 dollars
  • 40% of the time you win 5 dollars.

To compute the expected value, take note that a loss is negative while a win is positive.

[tex]E(X)=\sum_{i=1}x_1P(x_1)[/tex]

Therefore:

E(X)=(-20*0.3)+(-40*0.2)+(50*0.1)+(5*0.4)

E(X)=-7

  • The expected value of the event is -$7.
  • Based on the negative expectation, Bill should not play this game as he is expected to incur a loss.