Suppose 1 10,000 lottery tickets are issued, and each 5 yuan has 5 first prizes, 3 1.5 million yuan, 95 second prizes, 5,000 yuan, 900 third prizes, 300 yuan prizes, 9,000 fourth prizes and 20 yuan prizes.
Then the expected income from spending five dollars on lottery tickets is: 315000× 5/100000+5000× 95/1000000+300× 900/100000+20× 900.
This is obviously far less than 5 yuan.
Put all your eggs in one basket to buy lottery tickets, which means spending a lot of money on lottery tickets. Suppose you bought n tickets.
Then buy lottery tickets as an independent event, recorded as X 1.
Then the mathematical expectation of X 1+X2+ ... +Xn is 2.5n
Obviously, the more money you invest, the more money you may lose from the expected income.