3 colours, so prob each colour = 1/3
expected number of points
= (1/3)(40) + (1/3)(20) + (1/3)(0)
= 20
won?Black = 40
points
Gray = 20 points
White = 0 points
expected number of points
= (1/3)(40) + (1/3)(20) + (1/3)(0)
= 20
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.