How Many Combinations
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How Many Combinations

[From: ] [author: ] [Date: 11-12-23] [Hit: ]
your expected winnings on a ticket with 3 different digits is(1/1000)($500) + (5/1000)($40) = $0.70.So if each ticket costs 50 cents, on average you would gain 20 cents per ticket using the strategy of picking 3 different digits.If each ticket instead costs $1, on average you would lose 30 cents per ticket using the strategy of picking 3 different digits.......

Q2. Let's consider this question from a somewhat different viewpoint. Note that *not* all three-digit numbers are equally good to pick (assuming that the winning 3-digit number is of course randomly selected)! The best strategy is to pick a 3-digit number whose digits are all different, to maximize the probability of winning 40 dollars (note that any three-digit number picked results in the same probability of winning 500 dollars).

Ignoring the cost of a ticket, your expected winnings on a ticket with 3 different digits is
(1/1000)($500) + (5/1000)($40) = $0.70.

So if each ticket costs 50 cents, on average you would gain 20 cents per ticket using the strategy of picking 3 different digits.

If each ticket instead costs $1, on average you would lose 30 cents per ticket using the strategy of picking 3 different digits.

Note that if you pick all 1000 numbers, on average your profit is *less* than 200 dollars (if tickets cost $0.50 each), and on average your loss is *worse* than 300 dollars (if tickets cost $1 each). This is because the winning number may have some digits the same.

Lord bless you today!
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