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If you draw a card with a value of four or less from a standard deck of cards I will pay you $43 if not you pay me $10. Step 1. Find the expected value of the proposition and round the answer to two decimal places. Losses must be expressed as negative values. Step 2. If you play this game 755 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

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MrRoyal

The expected value of the game is its average earnings

  • The expected value of a round is $2.23
  • The expected value when the game is played 755 times is $1683.65

How to determine the expected value of a round

There are 12 cards with a value of 4 or less.

So, the probability of selecting a card with a value of 4 or less is:

[tex]P(x \le 4) = \frac{12}{52}[/tex]

The probability of selecting a card with a value more than 4 is the complement of the above probability.

So, we have:

[tex]P(x > 4) = 1 - \frac{12}{52}[/tex]

[tex]P(x > 4) = \frac{40}{52}[/tex]

The expected value is then calculated as:

[tex]E(x) = \frac{12}{52} * 43 - \frac{40}{52} * 10[/tex]

Evaluate

[tex]E(x) = \frac{12* 43 - 40 * 10}{52}[/tex]

[tex]E(x) = \frac{116}{52}[/tex]

Simplify

[tex]E(x) = 2.23[/tex]

Hence, the expected value of a round is $2.23

The expected value when the game is played 755 times

In (a), we have:

[tex]E(x) = 2.23[/tex]

In probability, we have:

[tex]E(nx) = n * E(x)[/tex]

So, we have:

[tex]E(755x) = 755 * 2.23[/tex]

[tex]E(755x) = 1683.65[/tex]

Hence, the expected value when the game is played 755 times is $1683.65

Read more about expected values at:

https://brainly.com/question/15858152

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