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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
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:
The probability of selecting a card with a value more than 4 is the complement of the above probability.
So, we have:
The expected value is then calculated as:
Evaluate
Simplify
Hence, the expected value of a round is $2.23
<h3>The expected value when the game is played 755 times</h3>In (a), we have:
In probability, we have:
So, we have:
Hence, the expected value when the game is played 755 times is $1683.65
Read more about expected values at:
First compute the area of the rectangle:
We have to find the radius of the circle:
circonférence of circle given radius is:
We get the equation:
Solving the above equation for r we get:
Compute the area of the circle like this:
The white area is the difference of the area of the rectangle and the area of the circle:
We have to find the radius of the circle:
circonférence of circle given radius is:
We get the equation:
Solving the above equation for r we get:
Compute the area of the circle like this:
The white area is the difference of the area of the rectangle and the area of the circle: