अनन्त बाँदर साध्य
|यो एउटा अनाथ (एक्लो) पृष्ठको रुपमा छ, यो पृष्ठ कुनै पनि पृष्ठसित नजोडिएको अथवा एक-दुइवटा वटासित मात्र जोडिएको हुन सक्छ। कृपया सम्बन्धित लेखबाट; यस पृष्ठसित लिङ्क जोड़्न सहायता गर्नुहोस् सुझाव यहाँ उपलब्ध हुनसक्छ। (अक्टोबर २०११)|
यसलाई नेपाली भाषामा गर्न आवश्यक छ। यसलाई नेपालीमा । नेपालीमा लेख्ने तरिका हेर्न यहाँ क्लिक गर्नुहोस्।
सोझो प्रमाण [सम्पादन गर्ने]
There is a straightforward proof of this theorem. If two events are statistically independent, then the probability of both happening equals the product of the probabilities of each one happening independently. For example, if the chance of rain in Montreal on a particular day is 0.3 and the chance of an earthquake in San Francisco on that day is 0.008, then the chance of both happening on that same day is 0.3 × 0.008 = 0.0024.
Suppose the typewriter has 50 keys, and the word to be typed is banana. If we assume that the keys are pressed randomly (i.e., with equal probability) and independently, then the chance that the first letter typed is 'b' is 1/50, and the chance that the second letter typed is a is also 1/50, and so on, because events are independent. Therefore, the chance of the first six letters matching banana is
- (1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6 = 1/15 625 000 000 ,
less than one in 15 billion. For the same reason, the chance that the next 6 letters match banana is also (1/50)6, and so on.
From the above, the chance of not typing banana in a given block of 6 letters is 1 − (1/50)6. Because each block is typed independently, the chance Xn of not typing banana in any of the first n blocks of 6 letters is
As n grows, Xn gets smaller. For an n of a million, Xn is roughly 0.9999, but for an n of 10 billion Xn is roughly 0.53 and for an n of 100 billion it is roughly 0.0017. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as is desired, This shows that the probability of typing "banana" in one of the predefined non-overlapping blocks of six letters tends to 1. In addition the word may appear across two blocks, so the estimate given is conservative.</ref> and the chance of typing banana approaches 100%.
सन्दर्भ [सम्पादन गर्ने]
- Isaac, Richard E. (1995), The Pleasures of Probability, Springer, pp. 48–50, ISBN 0-387-94415-X Isaac generalizes this argument immediately to variable text and alphabet size; the common main conclusion is on p.50.