[BruceZ]

[ QUOTE ]
Hey Bruce,

I don't understand this bit:

"The EV is the sum of the probabilities of each pair being selected, which is 10 times the probability that a particular pair is selected"

I have no clue how you deduced that, can someone elaborate?

[/ QUOTE ]

The EV of a number of things is always the sum of the probabilities of each thing. Let Xi be a random variable which = 1 if pair i is selected, and 0 if not. The expected value of the sum of Xi from 1 to 6 is the expected value of the number of pairs. This is the sum of Pi*1, where Pi is the probability that the ith pair is selected. All the Pi's are equal in this case since each pair has the same probability of being selected.

Here's an intuitive way to grasp this powerful concept. Suppose employee A works 7 days a week, employee B works 5 days a week, and employee C works 3 days a week, at random. What is the average number of employees on any given day? Well employee 1 is always there, so that's 1. B is there 5/7 of the time, and C is there 3/7 of the time, so the average is 1 + 5/7 + 3/7 = 2 1/7.