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 Post subject: Lottery
PostPosted: Wed, 20 Feb 2008 02:43:43 UTC 
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Hey! i'm having a lot of problems with one of my assignment question. I guess the major problem i have is that i don't really understand what it wants me to calculate =P hopefully someone can help.

Question:
Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on lottery every week. Chance of wining at the Florida’s pick 6 Lotto game is 1 in 23 million. Suppose you buy a $ 1 lottery ticket in anticipation of winning the $7 million grand prize Calculate your expected net winning. Interpret the results.

Thanks!!


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PostPosted: Wed, 20 Feb 2008 04:58:45 UTC 
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Expected net loss = $7,000,000*(1/23,000,000) - $1*(22,999,999/23,000,000)

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PostPosted: Wed, 20 Feb 2008 07:24:37 UTC 
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sean39: can you please explain how you came to this conclusion?


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PostPosted: Wed, 20 Feb 2008 12:27:13 UTC 
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I like to think of these questions as the following:
When are the odds as good as the payoff?

Here we stand to win 7mil instead of 23mil.

If the payoff was 23mil that would at least make the odds equal.

Sorry, I did not answer your question.


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PostPosted: Wed, 20 Feb 2008 12:45:53 UTC 
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thnx for the help! but then i don't get why u need to multiply the $1 by (22,999,999/23,000,000). Can you please explain that?


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 Post subject: Re: Lottery
PostPosted: Wed, 20 Feb 2008 13:44:54 UTC 
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Hello, xellenx!

Quote:
Chance of winning at the Florida’s Pick6 Lotto game is 1 in 23 million.
Suppose you buy a $ 1 lottery ticket in anticipation of winning the $7 million grand prize.
Calculate your expected net winning. Interpret the results.

Here is a rather primtive approach to an expectation problem . . .


Suppose you buy all 23,000,000 tickets. . This costs you: .\$23,000,000

. . In return, you will win the grand prize: .\$7,000,000

Your net winnings is: .\$7,000,000 - 23,000,000 \:=\:-\$16,000,000


Hence, your average winnings is: .$\frac{-\$16,000,000}{23,000,000} \;\approx\;-\$0.70


If you play this game regularly,
. . you can expect to lose an average of 70 cents per play.



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