Why Study Math? – The Odds of Becoming Rich

So you think you can strike it rich with the lotto? Well, maybe you can, but I have to tell you that the odds are not that good. In fact, according to mathematics your odds of winning are essentially nil. Understanding math and probability will allow you to calculate your probability of striking it rich in any given year, but then again maybe this knowledge might depress you somewhat: for the chance of you getting that big check is actually a lot less than your chance of being struck by lightning.

In mathematics, probability theory is that branch which teaches us to calculate the likelihood of all kinds of events. Coupled with its sister branch of statistics, probability theory renders a very powerful tool to make all kinds of predictions, from the probable next president of the United States to the likelihood that you will contract AIDS during your lifetime. Within the discipline of probability theory, one learns how to count and form combinations of items, and this counting is called combinatorial analysis. 사설토토사이트

Being able to count the combinations of things allows us to calculate things like the probability of hitting the Powerball Lotto. In doing so, this is where knowledge is sometimes painful, and we think of the poet’s famous words, “If ignorance is bliss, ’tis folly to be wise.” For the ignorant who do not understand the ramifications of probability theory, can be hopeful that their lotto tickets are the winners; whereas, we wise, suffer knowing that the chances are essentially nil.

Given this preamble, let’s compute the probability of your hitting the Powerball with your $1 dollar ticket. For this example, I will use the Megaball lottery game that is played in New Jersey and a few other states. In order to play, you must pick five numbers among 56 and then pick one megaball from among 46. The order in which the first five numbers come out is not important; if it were, your odds would be far, far worse. In order to win, you must match the five numbers, as well as match the chosen megaball. If you do this, you hit the “big one.” Nice thought, but what are the odds of your being so lucky?

Let’s compute the probability right now. In order to do this, understand that once you select your five numbers with the megaball, you have chosen one combination out of many, many others. In order to find your odds, we need to count how many other combinations there are. To do this we note that there are 56 numbers, and each one has an equally likely probability of being chosen. Once the first ball is chosen, then there are 55 others, all with the same probability of being selected. Once that one is chosen, there are 54, and so on.

If we think of five slots, then there are 56 balls that can go into the first slot; once chosen, there are 55 that can go into the second slot, then 54 in the third slot, down to 52 in the fifth slot. The number of ways we can do this is 56*55*54*53*52 = 458,377,920. Since the order chosen does not matter, we need to divide this number by a factor which is equal to 5*4*3*2*1 = 120. This is called the permutation factor. In other words, if you choose 1,5,6, 10, 25, then it does not matter whether the 5 is chosen first, last, or somewhere in between. In essence, this factor is telling us that the number of different ways, or permutations, of choosing five numbers is 120.

If we divide 458,377,920 by 120 we get 3,819,816. This is the number of 5-way combinations of the 56 balls, without regard to order of course. Now to get our final result, we have to remember that in order to hit the jackpot we still have to match the megaball. Since there are 46 of them, we need to multiply 3,819,816 by 46 to get 175,711,536. So your odds of winning are 1 in 175,711,536. Your probability of winning is 0.00000000569, which is essentially 0.

 

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