# अनन्त बाँदर साध्य

यसमा जानुहोस्: परिचालन, खोज्नुहोस्
टाइप गरिरहेको चिम्पान्जी

अनन्त बाँदर साध्य अनुसार एउटा बाँदरले एउटा टाइपराइटरमा यादृच्छिक रूपमा (randomly) टाईप गर्दै गयो भने अनन्तकाल (infinite time) सम्ममा विलियम शेक्सपियरको पूर्ण कृति टाइप गर्नु निस्चितप्राय हुन्छ।

 यो लेख वा खण्ड नेपाली भाषामा नभएर अर्को भाषामा लेखिएको छ। यसलाई नेपाली भाषामा उल्था गर्न आवश्यक छ। यसलाई नेपालीमा उल्था गर्नुहोस। नेपालीमा लेख्ने तरिका हेर्न यहाँ क्लिक गर्नुहोस्।

### सोझो प्रमाण

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

$X_n=\left(1-\frac{1}{50^6}\right)^n.$

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,[१] 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

1. 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.