1. Playing the Lottery 6/4/2016Copyright © 2010… REMTECH, inc … All Rights Reserved1 Probability Theory and the Lottery ● The Lottery picks numbers at random to see if you’ve won Matching Random Numbers is ALL About Probability Theory Probability Random Events (Click to Begin) ● A number, expressed as a fraction, that represents the likelihood an event will happen. ● You pick numbers for your lottery ticket – even if you have a reason for picking certain numbers, these can still be treated as random numbers. ● When the numbers you pick are related (for example, when you pick 5 numbers that can’t be duplicates, your picks Depend on each other to some degree), calculating the total probabilities of winning get more complex. Independent picks each carry their own odds, regardless of any other picks. Independent and Dependent Selections

2. Odds in a “Pick 3” Lottery Game Pick a number (type 0-9 in each of the “Your Picks” boxes), then click the Pick 3 button to simulate playing one lottery ticket, or click Pick All Year to play 52 times! 6/4/2016Copyright © 2010 … REMTECH, inc … All Rights Reserved2 (Click to Play Once) In this game, you pick a three digit number, and choose up to 4 different ways to win. Each way you play costs $1.00. The play options and payouts are based on existing state Pick 3 games, but Lotteries where you live may have different or additional options. Odds of winning Match all three in order – 1 in 1000 Match the first pair – 1 in 100 Match the last pair – 1 in 100 Match the first and last numbers – 1 in 100 (Click to Play 52 times) Select your Play Options Here - $1 each

3. Pick 3 Review 6/4/2016Copyright © 2010… REMTECH, inc … All Rights Reserved3 ● The probability of matching any given digit is proportional to how many digits you are selecting from. If you are choosing from 10 digits (0 to 9), the probability of matching your selection with the random number chosen is 1/10. ● If you are trying to match two or more Independent, Random digits, your total probability of matching is the Product of the all the individual probabilities. For matching two single digit numbers (0 to 9), your chance is (1/10) x (1/10), or 1/100 ● The odds (probability) of matching 2 numbers instead of 3 or more are greater for you, but the payout is proportionally less. (Click to Begin) ● Lottery games offer multiple ways to win. However, more choices do not mean better overall odds of winning.

4. Odds in the Mega Millions Lottery Game 6/4/2016Copyright © 2010 … REMTECH, inc … All Rights Reserved4 (Click to Play Once) Mega Millions has many ways to win. Your overall chances of winning something are 1 in 40, or 2.5% of the time. But having 9 possible ways to win might make it seem more likely to you. Ways to win, Prizes, and Approximate Odds No Yellow Ball Match Match 5 out of 5 – Win $250,000 – 1 / 3,904,701 Match 4 out of 5 – Win $150 – 1 / 15,313 Match 3 out of 5 – Win $7 – 1 / 306 With Yellow Ball Match Match 5 out of 5 – Win JACKPOT – 1 / 175,711,536 Match 4 out of 5 – Win $10,000 – 1 / 689,065 Match 3 out of 5 – Win $150 – 1 / 13,781 Match 2 out of 5 – Win $10 – 1 / 844 Match 1 out of 5 – Win $3 – 1 / 141 Match 0 out of 5 – Win $2 – 1 / 75 (Click to Play 52 times) Pick 5 numbers from 1 to 56, plus one bonus number (yellow ball) from 1 to 46 – or use the Easy Pick function to get a random selection for your picks. (Click to Generate Random Ticket)

5. Mega Millions Review 6/4/2016Copyright © 2010… REMTECH, inc … All Rights Reserved5 ● In the Pick 3 game, all the numbers were “independent” – your 2 nd number didn’t depend on what your 1 st choice was. In Mega Millions, your first 5 numbers are “dependent”, since you can’t pick duplicates. Your 2 nd pick “depends” on your 1 st, since they can’t be the same, etc. ● Your odds of matching are also more complicated – your 1 st number can match any of the 5 lottery picks, if your 1 st number matches one, then your 2 nd can match any of the other 4, and so on. So calculating your actual odds of winning gets complicated fairly quickly. ● The greater the odds, the greater the reward, but it is VERY unlikely you will ever win the Jackpot. If you bought 3 tickets a week, then on average you would win the Jackpot about once every 1 million years. (Click to Begin) ● Calculating your odds when many numbers are involved is more complex – especially when some of the numbers are related to each other.

6. Lottery Payouts 6/4/2016Copyright © 2010… REMTECH, inc … All Rights Reserved6 ● If you win a small amount, you are usually paid that full amount when you turn in your ticket at your local ticket sales agent. For larger amounts, you may have to wait for a check from the state, even if it’s an “Instant” Lottery. The cutoff varies by state, but usually if you win $500 or more then some taxes may be withheld. If taxes are not withheld, you are still responsible for reporting your winnings as income and paying the appropriate taxes on them. (Click to Begin) ● Large jackpot amounts are never paid out immediately in the amount advertised. The size of a jackpot is usually related to its “Future Value” in about 25 years. [See TimeMAPS™ Lesson 3.4 – The Time Value of Money] If you elect the Lump Sum amount to be paid up front, you will only get the amount that would earn you the whole Jackpot amount if interest were compounded over 25 years. ● In our Mega Millions example, if you won $1 million and took the yearly payout, you would get about $40,000 per year for 25 years BEFORE taxes.

7. Lottery Myths 6/4/2016Copyright © 2010… REMTECH, inc … All Rights Reserved7 ● Myth #1 – playing the same numbers every week gives you a better chance of winning. FALSE – Winning numbers are selected randomly at every drawing. What you played last week or what you will play next week has NO AFFECT on what happens this week. (Click to Begin) ● Myth #2 – by tracking past results, you can predict which numbers are more likely to be drawn in the future. FALSE – again, each drawing is a completely random event, and what has happened in the past has NO AFFECT on what happens in the future. ● Myth #3 – playing your own numbers is better than playing the “Easy Pick” or “Quick Pick” numbers generated by the ticket machine. FALSE – once again, these are all RANDOM numbers, any combination is equally likely to win (or lose).