There is an equally likely chance that a falling dart will land anywhere on the rug below. The following system is used to find the number of points the player wins. What is the expected value for the number of points

3 colours, so prob each colour = 1/3

expected number of points
= (1/3)(40) + (1/3)(20) + (1/3)(0)
= 20

What they said

24

To find the expected value for the number of points won, we need to multiply each possible outcome by its respective probability, and then sum up the results.

In this case, we have three possible outcomes: Black (40 points), Gray (20 points), and White (0 points). Since it's given that there is an equally likely chance for the dart to land anywhere on the rug, we can assume that each outcome has a probability of 1/3.

To calculate the expected value, we use the formula:

Expected value = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + ...

Substituting the values:

Expected value = (40 * 1/3) + (20 * 1/3) + (0 * 1/3)

Simplifying the equation:

Expected value = (40/3) + (20/3) + (0/3)

Expected value = 60/3

Expected value = 20

Therefore, the expected value for the number of points won is 20.