Thus, we asked ourselves two questions:
- What is the probability that there will be no winner in tonight's drawing?
- What is the probability that there will only be one sole winner?
The first summarizes the probabilities of: 0 to 8 individual winning tickets. As shown, the probability of not having a winner tonight and rolling over again drops from 18% to 3% as ticket sales increase from 300 million to 600 million. Similarly, we can see that the probability of having a single winner decreases from 39% to 27%, while that of two winners decreases slightly from 28% to 26%. Interestingly, we find the probabilities of 3 to 5 winners rapidly increase as sales approach 600 million. We believe the likelihood that 6 or more winning combinations will be sold is rather slim.
|Table 1: Probability of Mega Millions Winning Tickets|
|Winning Tickets||300M Sold||400M Sold||500M Sold||600M Sold|
|None, No winner||18.1%||10.3%||5.8%||3.3%|
|1 Winner Only||39.3%||35.4%||31.2%||27.4%|
|2 Winner Only||28.2%||29.5%||28.2%||25.9%|
The second table summarizes the distribution of the tickets sold. It estimates the absolute number of tickets in each category. Here we find that approximately 31.9 million combinations will not be generated when sales are at the 300M level, but only 5.8 million combinations will be unsold when 600M tickets are printed. In all other cases, the absolute number of tickets per category increase as sales increase. Interestingly enough, we can see how the size of the 6 and 7 tuplets begins to grow.
|Table 2: Distribution of Mega Millions Tickets Sold|
|Numbers||300M Sold||400M Sold||500M Sold||600M Sold|
|1 Only (Singles)||143,846,803||157,675,257||165,502,526||169,932,970|
We wish everyone the best of luck tonight and hope your dreams come true. But, as we can see from the above, remember to set your expectations according to the probability that you may have to share the jackpot prize with somebody else.