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# Mega millions jackpot probability

Probability of winning the Mega Millions jackpot. Created by Sal Khan.

## Want to join the conversation?

• Since the winnings are much greater than \$176 million, doesn't this mean that it would be reasonable to buy 176 million tickets, guaranteeing that you make a profit of ~\$300 million?
• An Australian investment group tried this a few years ago. They paid a lot of people to buy up a lot of tickets for them. They didn't buy enough to guarantee the jackpot win, but still made millions in profit on lesser prizes.
• How was the probability of being struck by a lightning calculated? Because 1/10,000 doesn't sound like a lot.
• National Weather Service did the calculation based on reports provided to them: http://www.lightningsafety.noaa.gov/medical.htm

ODDS OF BECOMING A LIGHTNING VICTIM
(based on averages for 2001-2010)

Estimated U.S. population as of 2011

310,000,000

Annual Number of Deaths Reported

39

Number of Injuries Reported

241

Estimated number of U.S. Deaths

40

Estimated number of actual Injuries

360

Odds of being struck by lightning in a given year (reported deaths + injuries)

1/1,000,000

Odds of being struck by lightning in a given year (estimated total deaths + injuries)

1/775,000

1/10,000

Odds you will be affected by someone being struck (Ten people affected for every one struck)

1/1000
• Isn't odds the same as probability?
• does buying more than one tickets increase (mathematically of course) a person's odds of winning. 1 vs 100 tickets. thanks
• Yes. Assuming all the tickets have different numbers, if you have 100 tickets, you have 100 times the chance of winning.
• Where can I find a video about which to choose: a lump sum or getting money over time?
• I'm not sure if there's one here, but it's a net present value calculation.
• Hi,
I'm just curious why you multiply by 46 and not (1/46)?
To my understanding, choosing the correct super ball from the bin of 46 would only be one possible outcome of a total possible 46 balls in the bin...
• Hello, sorry your question has gone unanswered for so long. This is my understanding of the situation. You may not have realized that when Sal Khan multiplied by 46 he was working in the denominator. Sal multiplied the denominator by 46 which is essentially multiplying by 1/46. This is what Sal did:
``      1               1   —————————————— = ———————————3,819,816 x 46   175,711,536``
This is the same thing as what Sal did, just combining them in a different order:
``    1       1         1————————— x —— = ———————————3,819,816   46   175,711,536``
I hope this helps!
• If the odds of selecting a winning lotto number is 1 : 177M and a ticket is \$1. Once the jackpot is over 177M + tax + interest on loan, why not take out a loan and buy every ticket?! Betting on the chance that you don't split the winnings with anyone this is a minimal risk "investment."
• Hmm. There is an old saying, the lottery is a tax on people who didn't think they would need algebra in real life.

Given how many tickets are sold when the lottery gets that large, there is an excellent chance of more than one winner.

BTW, you'll notice that they make it physically impossible to play all possible numbers. Even if you somehow managed to play 10 sets of numbers a second, round the clock, non-stop, it would take you over 200 days to play all of possible combinations, though most lotteries only give you a few days to buy tickets.

Thus, it absolutely impossible to buy every combination for the large pay-off lotteries. That is not by accident.
• So let's say I own a surfboard-making shop, and it's a very good shop. Only one in 1000 boards is messed up. I also have a test which is 99% accurate. If my surfboard tests bad, then what is the probability that it is bad? How would I go about doing something like this?
• Assuming that the boards are all tested independently and that problems making boards occur independently, a board that tests as being bad is 99% likely to actually be bad - the probability should be the same as the accuracy of the test.

It's slightly more complicated if you consider something like the probability of selling a bad board, which should be about 1 per 100,000 -- which is 1/1000 for the chance of it actually being bad, multiplied by the 1/100 chance of it wrongly passing the test. 99 bad boards from that 100,000 would be found and not sold (99/100 detected x 1/1000 bad), while around 100 good boards would test bad (1/100 wrong tests x 999/1000 good boards).