Lottery games are very popular, but what are the actual probabilities

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Lottery Games Statistics
Celyese1
Lottery games are very popular, but what are the actual probabilities that a ticket purchased is going to win? Calculate the probability of winning some of the more popular games.
 A game that draws 3 digits from 09 from three separate machines.
 What is the probability of winning a “straight” bet by matching the three digits in the exact order?
 What is the probability of winning a “box” bet by matching the three digits in any order?
 What is the probability of not matching any numbers on a ticket?
 A game that draws 4 digits from 09 from four separate machines.
 What is the probability of winning a “straight” bet by matching the four digits in the exact order?
 What is the probability of winning a “box” bet by matching the four digits in any order?
 What is the probability of not matching any numbers on a ticket?
 A game that draws 5 digits from 149 from the same machine. In other words, numbers are drawn and not replaced.
 What is the probability of winning the jackpot by matching all 5 numbers?
 What is the probability of winning a major prize by matching 4 of the 5 numbers? Make the calculation assuming the first 4 values are matched and the fifth one does not.
 What is the probability of not matching any numbers on a ticket?
 A supermegajackpot game that draws 6 numbers from 1 – 70 from a single machine and then a SuperMegaMatch ball numbered 1 – 30 from a separate machine.
 What is the probability of winning the SuperMega jackpot by matching all six numbers and the SuperMegaMatch ball?
 What is the probability of winning the jackpot by matching all six numbers, but not matching the SuperMegaMatch ball?
 What is the probability of not matching any numbers on a ticket.
 State run lottery games tend to pay out 50% of what the odds against winning are, rounded up. For instance, if the odds against winning in a game are 499 : 1, the lottery game will pay $250 for a winning $1 ticket. This is how the lottery raises money for the state. Complete the table below with predicted payout values for winning $1 bets using this formula.
3Digit Drawing
4Digit Drawing
5Number Drawing
SuperMega Drawing
Straight win:
Straight win:
Match 5:
SuperMega Jacpot
Boxed win:
Boxed win:
Match 4:
Jackpot:
Show all work and express the probabilities as both fractions and decimal values. Use scientific notation where appropriate.
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