Question 1102726
Look at all of the possible outcomes, 30 of them,
(1,1)(1,2)(1,2)(1,3)(1,3)
(1,1)(1,2)(1,2)(1,3)(1,3)
(2,1)(2,1)(2,2)(2,3)(2,3)
(2,1)(2,1)(2,2)(2,3)(2,3)
(3,1)(3,1)(3,2)(3,2)(3,3)
(3,1)(3,1)(3,2)(3,2)(3,3)
and their sums,
2,3,3,4,4
2,3,3,4,4
3,3,4,5,5
3,3,4,5,5
4,4,5,5,6
4,4,5,5,6
So then look at the frequency of each sum,
2:2
3:8
4:10
5:8
6:2
Then the probabilities would be,
2:{{{2/30=1/15}}}
3:{{{8/30=4/15}}}
4:{{{10/30=1/3}}}
5:{{{8/30=4/15}}}
6:{{{2/30=1/15}}}
So,
{{{E=2(1/15)+3(4/15)+4(1/3)+5(4/15)+6(1/15)}}}
{{{E=2/15+12/15+20/15+20/15+6/15}}}
{{{E=60/15}}}
{{{E=4}}}