Question

2. A box contains 50 slips of paper. Forty of the slips are marked $0, 8 of the slips are marked $20, 1 slip is marked $100, and the last one is marked $500. Find the expected net winnings of a person who pays $10 to randomly select one slip of paper. Interpret.

Answer 1

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