Probability Basics (Simplifying Math) 

impressive upload Eric Buffington. I smashed the thumbs up on your video. Maintain up the solid work.

please Mr.Eric could you please give every vedio a Unique serial No. to facilitate following your veios in a series I want to watch the next vedio but I don't know which one I have to watch finally .Thanks a lot for your invaluabe effort

Mr. Buffington can you help me with this problem. Tim rolls a pair of dice 25 times and records the sum of the numbers shown. How many different sums are possible?

There was a probability question for one on my certification tests. (If someone spins the spinner twice, what is the probability it will land on an even number? The spinner consisted of the numbers 1,2,2,3,4,4,5. My answer was 16/49, but it was not one of the choice answers. How would you figure this out? Reply

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The mathematical probability of Evolution According to the most-widely accepted theory of evolution today, the sole mechanism for producing evolution is that of random mutation combined with natural selection. Mutations are random changes in genetic systems. Natural selection is considered by evolutionists to be a sort of sieve, which retains the "good" mutations and allows the others to pass away. Since random changes in ordered systems almost always will decrease the amount of order in those systems, nearly all mutations are harmful to the organisms which experience them. Nevertheless, the evolutionist insists that each complex organism in the world today has arisen by a long string of gradually accumulated good mutations preserved by natural selection. No one has ever actually observed a genuine mutation occurring in the natural environment which was beneficial (that is, adding useful genetic information to an existing genetic code), and therefore, retained by the selection process. For some reason, however, the idea has a certain persuasive quality about it and seems eminently reasonable to many people-until it is examined quantitatively, that is! For example, consider a very simple putative organism composed of only 200 integrated and functioning parts, and the problem of deriving that organism by this type of process. The system presumably must have started with only one part and then gradually built itself up over many generations into its 200-part organization. The developing organism, at each successive stage, must itself be integrated and functioning in its environment in order to survive until the next stage. Each successive stage, of course, becomes statistically less likely than the preceding one, since it is far easier for a complex system to break down than to build itself up. A four-component integrated system can more easily "mutate" (that is, somehow suddenly change) into a three-component system (or even a four-component non-functioning system) than into a five-component integrated system. If, at any step in the chain, the system mutates "downward," then it is either destroyed altogether or else moves backward, in an evolutionary sense. Therefore, the successful production of a 200-component functioning organism requires, at least, 200 successive, successful such "mutations," each of which is highly unlikely. Even evolutionists recognize that true mutations are very rare, and beneficial mutations are extremely rare-not more than one out of a thousand mutations are beneficial, at the very most. But let us give the evolutionist the benefit of every consideration. Assume that, at each mutational step, there is equally as much chance for it to be good as bad. Thus, the probability for the success of each mutation is assumed to be one out of two, or one-half. Elementary statistical theory shows that the probability of 200 successive mutations being successful is then (½)200, or one chance out of 1060. The number 1060, if written out, would be "one" followed by sixty "zeros." In other words, the chance that a 200-component organism could be formed by mutation and natural selection is less than one chance out of a trillion, trillion, trillion, trillion, trillion! Lest anyone think that a 200-part system is unreasonably complex, it should be noted that even a one-celled plant or animal may have millions of molecular "parts." The evolutionist might react by saying that even though any one such mutating organism might not be successful, surely some around the world would be, especially in the 10 billion years (or 1018 seconds) of assumed earth history. Therefore, let us imagine that every one of the earth's 1014 square feet of surface harbors a billion (i.e., 109) mutating systems and that each mutation requires one-half second (actually it would take far more time than this). Each system can thus go through its 200 mutations in 100 seconds and then, if it is unsuccessful, start over for a new try. In 1018 seconds, there can, therefore, be 1018/102, or 1016, trials by each mutating system. Multiplying all these numbers together, there would be a total possible number of attempts to develop a 200-component system equal to 1014 (109) (1016), or 1039 attempts. Since the probability against the success of any one of them is 1060, it is obvious that the probability that just one of these 1039 attempts might be successful is only one out of 1060/1039, or 1021. All this means that the chance that any kind of a 200-component integrated functioning organism could be developed by mutation and natural selection just once, anywhere in the world, in all the assumed expanse of geologic time, is less than one chance out of a billion trillion. What possible conclusion, therefore, can we derive from such considerations as this except that evolution by mutation and natural selection is mathematically and logically indefensible!