Explanation and answer:
If if the possible outcomes are xi, and the corresponding probability is pi, where i is one of the N events, then the expectation [E] is given by
[E] = sum (xi*pi)
In the given case, n= frequency of the event, N=50=total number of events
i n xi pi n*xi*pi
1 40 0 40/50 40*0*40/50 = 0
2 8 20 8/50 8*20/50 = 3.20
3 1 100 1/50 1*100/50 = 2.00
4 1 500 1/50 1*500/40= 10.00
Total (expected gross winning) = 15.20
Person has already paid $10,
so the expected net winning = 15.20 - 10 = 5.20
