Lottery Winnings: calculate expected net winnings

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Tascja

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Hello, more difficulty with my probability assignment, please please help. What formulas would I use?

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 winning at the Georgia'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.

Thank you greatly for your assistance.
 
Re: Lottery Winnings

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 winning at the Georgia'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.
Click to expand...

Odds of winning times what you win, plus odds of losing times what you lose, minus the cost of playing:

(1/23,000,000)($7) + [(23,000,000 – 1)/(23,000,000)]($0) - $1 = ?

Make sense?
 
Re: Lottery Winnings

I've been working on the question since I posted it and I found this:

odds: 1in 23million
there are 6 possibilities: 6! = 720
therefore odds are 23million/720 = 31,944 to one

probability of winning with $1 = 1/31,944 = 0.00031304
probability of losing = 1 - 0.00031304 = .99997

Expected return = (potential winning * probability of winning) - (potential cost * probability of losing)
= (7,000,000 * 0.00031304) - (1 * .99997)
= 218.1283

in terms of results, a winning of $218 dollars sounds like too much. where did I go wrong?
 
Expected return = (potential winning * probability of winning) - (potential cost * probability of losing)
Click to expand...

This statement above is generally correct, but I have some comments on your calcs:
1) They've already provided the odds of winning in the problem statement, so no need for the 6!, etc.
2) The potential cost of losing is $0; the $1 ticket price is not "potential" cost; it is always an actual cost whether one wins or loses.
 
wjm11, thank you for your continued help. i really appreciate it :) thank you.
 
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