A lottery has a $1 000 000 first prize, a $25 000 second prize, and five $1000 third prizes. A total of 2 000 000 tickets are sold.
a) what is the probability of wining of a prize in this lottery ??
b)if a ticket costs $2.00, what is the expected profit per ticket ??
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2007-01-11 08:50:06 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Odds of winning are 7:2,000,000 = 0.00035% (7 winners out of 2 million entries)
For every $2 ticket, the expected profit is -$1.49 (everyone loses $2, 1 chance in 2 mil of winning $1 mil, 1 chance in 2 mil of winning $25k, 5 chances in 2 mil of winning $1k --- EV = -2 * 2,000,000 / 2,000,000 + 1,000,000 * 1 / 2,000,000 + 25,000 * 1 / 2,000,000 + 1,000 * 5 / 2,000,000 = -1.485
2007-01-11 09:00:45 · answer #1 · answered by devilben 2 · 2⤊ 0⤋
There are 7 possible prizes.
2,000,000 people enter.
Thus it's a 7 in 2,000,000 probability.
2 x 2,000,000 tickets is 4000000 dollars.
Subtract 1000000,25000 and 5000
$2970000 profit
2007-01-11 17:00:18 · answer #2 · answered by Anonymous · 0⤊ 1⤋
The first answerer calculated the profit for the people running the lottery.
The second answerer calculated the expection of someone who buys a ticket.
2007-01-11 17:03:22 · answer #3 · answered by modulo_function 7 · 1⤊ 1⤋