How to Calculate Powerball Odds

How to Calculate Powerball Odds Powerball is a multistate lottery that is quite popular due to its multimillion-dollar jackpots. Some of these jackpots reach values that are well over $100 million. An interesting quest ion from a probabilistic  sense is, â€Å"How are the odds calculated on the likelihood of winning Powerball?† The Rules First we will examine the rules of Powerball as it is currently configured. During each drawing, two drums full of balls are thoroughly mixed and randomized. The first drum contains white balls numbered 1 to 59. Five are drawn without replacement from this drum. The second drum has red balls that are numbered from 1 to 35. One of these is drawn. The object is to match as many of these numbers as possible. The Prizes The full jackpot is won when all six numbers selected by a player match perfectly with the balls that are drawn. There are prizes with lesser values for partial matching, for a total of nine different ways to win some dollar amount from Powerball. These ways of winning are: Matching all five white balls and the red ball wins the grand prize jackpot. The value of this varies depending upon how long it has been since someone has won this grand prize.Matching all five white balls but not the red ball wins $1,000,000.Matching exactly four of the five white balls and the red ball wins $10,000.Matching exactly four of the five white balls but not the red ball wins $100.Matching exactly three of the five white balls and the red ball wins $100.Matching exactly three of the five white balls but not the red ball wins $7.Matching exactly two of the five white balls and the red ball wins $7.Matching exactly one of the five white balls and the red ball wins $4.Matching just the red ball but none of the white balls wins $4. We will look at how to calculate each of these probabilities. Throughout these calculations, it is important to note that the order of how the balls come out of the drum is not important. The only thing that matters is the set of balls that are drawn. For this reason our calculations involve combinations and not permutations. Also useful in every calculation below is the total number of combinations that can be drawn. We have five selected from the 59 white balls, or using the notation for combinations, C(59, 5) 5,006,386 ways for this to occur. There are 35 ways to select the red ball, resulting in 35 x 5,006,386 175,223,510 possible selections. Jackpot Although the jackpot of matching all six balls is the most difficult to obtain, it is the easiest probability to calculate. Out of the multitude of 175,223,510 possible selections, there is exactly one way to win the jackpot. Thus the probability that a particular ticket wins the jackpot is 1/175,223,510. Five White Balls To win $1,000,000 we need to match the five white balls, but not the red one. There is only one way to match all five. There are 34 ways to not match the red ball. So the probability of winning $1,000,000 is 34/175,223,510, or approximately 1/5,153,633. Four White Balls and One Red For a prize of $10,000, we must match four of the five white balls and the red one. There are C(5,4) 5 ways to match four of the five. The fifth ball must be one of the remaining 54 that were not drawn, and so there are C(54, 1) 54 ways for this to happen. There is only 1 way to match the red ball. This means that there are 5 x 54 x 1 270 ways to match exactly four white balls and the red one, giving a probability of 270/175,223,510, or approximately 1/648,976. Four White Balls and No Red One way to win a prize of $100 is to match four of the five white balls and not match the red one. As in the previous case, there are C(5,4) 5 ways to match four of the five. The fifth ball must be one of the remaining 54 that were not drawn, and so there are C(54, 1) 54 ways for this to happen. This time, there are 34 ways to not match the red ball. This means that there are 5 x 54 x 34 9180 ways to match exactly four white balls but not the red one, giving a probability of 9180/175,223,510, or approximately 1/19,088. Three White Balls and One Red Another way to win a prize of $100 is to match exactly three of the five white balls and also match the red one. There are C(5,3) 10 ways to match three of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 2) 1431 ways for this to happen. There is one way to match the red ball. This means that there are 10 x 1431 x 1 14,310 ways to match exactly three white balls and the red one, giving a probability of 14,310/175,223,510, or approximately 1/12,245. Three White Balls and No Red One way to win a prize of $7 is to match exactly three of the five white balls and not match the red one. There are C(5,3) 10 ways to match three of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 2) 1431 ways for this to happen. This time there are 34 ways to not match the red ball. This means that there are 10 x 1431 x 34 486,540 ways to match exactly three white balls but not the red one, giving a probability of 486,540/175,223,510, or approximately 1/360. Two White Balls and One Red Another way to win a prize of $7 is to match exactly two of the five white balls and also match the red one. There are C(5,2) 10 ways to match two of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 3) 24,804 ways for this to happen. There is one way to match the red ball. This means that there are 10 x 24,804 x 1 248,040 ways to match exactly two white balls and the red one, giving a probability of 248,040/175,223,510, or approximately 1/706. One White Ball and One Red One way to win a prize of $4 is to match exactly one of the five white balls and also match the red one. There are C(5,4) 5 ways to match one of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 4) 316,251 ways for this to happen. There is one way to match the red ball. This means that there are 5 x 316,251 x1 1,581,255 ways to match exactly one white ball and the red one, giving a probability of 1,581,255/175,223,510, or approximately 1/111. One Red Ball Another way to win a prize of $4 is to match none of the five white balls but match the red one. There are 54 balls that are not any of the five selected, and we have C(54, 5) 3,162,510 ways for this to happen. There is one way to match the red ball. This means that there are 3,162,510 ways to match none of the balls except for the red one, giving a probability of 3,162,510/175,223,510, or approximately 1/55. This case is somewhat counterintuitive. There are 36 red balls, so we may think that the probability of matching one of them would be 1/36. However, this neglects the other conditions imposed by the white balls. Many combinations involving the correct red ball also include matches on some of the white balls as well.

Nissan Altima Electric Mode Hybrid Car Question

Nissan Altima Electric Mode Hybrid Car Question Hello Christine and Scott, I was very relieved to find your pages under About.com and find out I could email you. A few weeks ago we purchased a 2008 Nissan Altima Hybrid and recently we noticed something that has us worried: the gasoline engine kicks on a few seconds after starting the car and while the car is still in PARK. It stays on EV MODE for only the first few seconds. This is not what we expected! We thought (from research) that the high voltage battery would have total control at startup, low speeds, and when not moving (at a stop sign /red light). In other words, NO GASOLINE being used at these times. EV MODE the whole time! We also observed: 1. After we shift to D, DRIVE, it happens again every time the vehicle comes to a full stop while at a stop sign or red light and were not moving for more than a few seconds. 2. The engine stays on for at least a minute and then shuts off, EV MODE resumes and all is quiet until I start moving and accelerating. 3. This behavior seems to happen when the engine is cold, in other words, when it hasnt been used for hours (e.g. first drive in the morning) and keeps happening for about 1/2 hour or so during that first drive. After 1/2 hour or so, this stops happening. In other words, the EV MODE sign comes on and STAYS ON the whole time the car is stopped (idle) at a stop sign/red traffic light or while the car is in PARK but still on. This is what we thought would ALWAYS happen! 4. There is one exception to what I just said in item 3 above. Today for the first time, while at a red light, and after the car went into EV MODE, the engine kicked on even though I had just driven the car for at least one hour at high speeds on highway. Is something wrong with my car? I noticed on your website that you own your own 2008 Nissan Hybrid. Please tell me whats happening with yours. At first my husband thought that this was due to the cold weather (under 40 degrees). But today, the temperature was at 48 degrees and it still didnt stay in EV MODE at startup. Please help. I am afraid this might be a defective car. Dora PS. Yesterday I drove the car to the dealer and the salesperson that sold us the car told us that he has seen it happen before and that it is normal. He even had me drive another hybrid (2007) that had not been sold yet and sure enough, seconds after the car started, the EV MODE signal disappeared and the engine started EVEN THOUGH I was still in park mode. I dont know whether to believe him or not. I also dont find any info on manual to either identify this behavior as normal or not normal. Hey Dora, Thanks for writing - good questions. We understand your concerns. No worries – it sounds as if your 2008 Altima Hybrid is working perfectly normally. Your husband is right - it does have a lot to do with the cold temperatures, and there actually are several conditions that will make the engine on your car run, regardless of your input. They are: State of battery charge Temperature of the engine and hybrid components Ambient air temperature When you start the car, it will usually start the engine after just a few seconds, even if its been only a few hours since youve last driven it. The computer does this automatically to warm the engine, hybrid battery and associated hybrid components. Under mild weather conditions, the engine should shut off after just a few minutes, but when it’s colder out, it could take substantially longer- it also depends upon the amount of charge left in the hybrid battery. If it’s on the low side, the engine may continue running to charge the battery up to full capacity. Also, and this is especially true in the winter (and if you are using the heater and/or the defroster a lot), the engine will run longer. The engine has to run to warm the cabin- and the higher you have the heat set (and the longer it’s on), the more the engine will run. If you have electrically heated seats, using those can help minimize the need to heat the cabin air as much, thus minimizing the engine ru nning time also. Even if you are stopped for a minute or more at a traffic light and the car is in EV mode, if any of these conditions come up (low battery, car needing heat), the engine will start. Again, all of this is normal. You’ll notice as we get into spring and early summer (and you won’t be needing the heat/defroster as much), everything will come up to operating temperature quicker and the Altima Hybrid will stay in EV mode much longer. In the summertime when it gets really hot and you’re using the AC a lot, you could notice that it runs the engine more. The AC compressor runs off electricity, so you may find the engine kicks on more often to keep the battery charged. Just bear in mind that this is a hybrid electric car and is reliant upon the gasoline engine to keep the entire system up and running. Even though you can drive in electric mode, it’s still more of an assistant than a main power source. Your Altima uses Toyota’s Synergy Drive System- in our opinion, it is the best one available. As you get used to this car, we bet you’ll not only be able to maximize the EV mode driving (and fuel economy), but come to love it as well. For your reference, here’s an article we wrote about hybrids and cold temps, and some info about obtaining the best mileage from your hybrid via hypermiling. (Yep, Scott hypermiled in the Altima Hybrid- look what it can do. Thanks for visiting our site and writing- please feel free to let us know if you have any more questions. Best regards, Christine Scott