Consider two lotteries, where a player can buy a ticket, scratch it, and has a possibility to win a prize. Lottery A: 10000 tickets total, 1000 tickets win $1 each, 100 tickets win $10 each, 10 tickets win $100 each, and the other tickets win nothing. Lottery B: 20000 tickets total, 100 tickets win $20 each, 10 tickets win $300 each, 1 ticket wins $1000, and the other tickets win nothing.

(a) For each of the lotteries, find the expectation and the standard deviation of the prize that a player can win if he buys 1 ticket.

(b) Taking into account only the expectation and the standard deviation of the prize, give an argument why a player may prefer playing Lottery A to playing Lottery B, and an argument why he may prefer playing Lottery B to playing Lottery A.