Question

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Answer 1

6 numbers are possible1,2,3,4,5,6
P(X=2)=1/15
P(X=3)=2/15
P(X=4)=3/15
P(X=5)=4/15
P(X=6)=5/15
X P(X)
2 1/15
3 2/15
4 3/15
5 4/15
6 5/15
E=`sum` X&P(x)
=`2*1/15+3*2/15+4*3/15+5*4/15+6*5/15`
=`70/15=14/3`