Question 227876
this looks like it addresses your problem <a href = "http://wilcoxen.maxwell.insightworks.com/pages/126.html" target = "_blank">Expected Value</a>


In your problem, the probability and the payoffs are as follows:


p(red) = 3/10 = .3
p(blue) = 4/10 = .4
p(yellow) = 2/10 = .2
p(green) = 1/10 = .1


Sum of all probabilities equals 1 which it should.


$4.00 payoff for red * .3 = $1.20
$2.00 payoff for green * .1 = $.20

$2.00 payback for blue * .4 = -$.80
$3.00 payback for yellow * .2 = -$.60


Expected Value would be the sum of these = 1.2 + .2 - .8 - .6 = 1.4 - 1.4 = 0


The spinner can expect to break even in the long run.