contestada

14) A carnival has set up the following game. You are blindfolded and have to pick a coin from 9 pennies, 8
nickels, 12 dimes, 16 quarters, 11 half-dollars, and 4 dollar pieces. It costs a quarter to play the game. What
could you be expected to win or lose every time you play the game?

Respuesta :

Using the expected value, it is found that you should be expected to win $0.0032 every time you play the game.

  • A probability is the number of desired outcomes divided by the number of total outcomes.
  • The expected value is given by the sum of each value multiplied by it's respective probability.

9 + 8 + 12 + 16 + 11 + 4 = 60

  • In total, there are 60 coins.

Considering the cost of $0.25, the probability of each monetary outcome when one coin is chosen is:

[tex]P(X = -0.24) = \frac{9}{60}[/tex]

[tex]P(X = -0.20) = \frac{8}{60}[/tex]

[tex]P(X = -0.15) = \frac{12}{60}[/tex]

[tex]P(X = 0) = \frac{16}{60}[/tex]

[tex]P(X = 0.25) = \frac{11}{60}[/tex]

[tex]P(X = 0.75) = \frac{4}{60}[/tex]

Hence, the expected value is:

[tex]E(X) = -0.24\frac{9}{60} - 0.2\frac{8}{60} - 0.15\frac{12}{60} + 0\frac{16}{60} + 0.25\frac{11}{60} + 0.75\frac{4}{60}[/tex]

[tex]E(X) =  \frac{-0.24(9) - 0.2(8) - 0.15(12) + 0(16) + 0.25(11) + 0.75(4)}{60} = 0.0032[/tex]

You should be expected to win $0.0032 every time you play the game.

A similar problem is given at https://brainly.com/question/24855677

Otras preguntas