Posted: August 6th, 2022

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 0-9 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 0-9 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 1-49 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 super-mega-jackpot game that draws 6 numbers from 1 – 70 from a single machine and then a Super-Mega-Match ball numbered 1 – 30 from a separate machine.
- What is the probability of winning the Super-Mega jackpot by matching all six numbers and the Super-Mega-Match ball?
- What is the probability of winning the jackpot by matching all six numbers, but not matching the Super-Mega-Match 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.

**3-Digit Drawing**

**4-Digit Drawing**

**5-Number Drawing**

**Super-Mega Drawing**

Straight win:

Straight win:

Match 5:

Super-Mega 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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