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Sagot :
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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