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 won?
Black = 40 points
Gray = 20 points
White = 0 points
To find the expected value for the number of points won, we need to assign probabilities to each outcome and multiply those probabilities by the corresponding points.
In this case, there are three possible outcomes: landing on black (40 points), gray (20 points), or white (0 points). Since it is mentioned that there is an equally likely chance of the dart landing anywhere on the rug, we can assume that each outcome has a probability of 1/3 (or 33.33%).
To calculate the expected value, we multiply each outcome by its corresponding probability and sum them up:
Expected value = (Probability of black * Points for black) + (Probability of gray * Points for gray) + (Probability of white * Points for white)
= (1/3 * 40) + (1/3 * 20) + (1/3 * 0)
= 40/3 + 20/3 + 0
= 60/3
= 20
Therefore, the expected value for the number of points won is 20.