50 Mathematical Ideas You Really Need to Know

Four colours will be enough ...

31 Probability What is the chance of it snowing tomorrow? What is the likelihood that I will catch the early train? What is the ...

while 0.9 would signify a high probability. Origins of probability The mathematical theory of probability came to the fore in th ...

Sample space (for 2 dice) Let’s consider the ‘event’ A of getting the sum of the dice to add up to 7. There are 6 combinations t ...

The monkey on a typewriter Alfred is a monkey who lives in the local zoo. He has a battered old typewriter with 26 keys for the ...

the probability of all occurrences is 1 probability has a value which is greater than or equal to zero when occurrences cannot ...

32 Bayes’s theory The early years of the Rev. Thomas Bayes are obscure. Born in the southeast of England, probably in 1702, he b ...

Venn diagram showing the logical structure of the appearance of spots and measles This tells Dr Why that there are x patients wh ...

addressed by Bayes in his essay. To work out the probabilities we need to put in some numbers. These will be subjective but what ...

interpreting probability as degrees of belief or, as it is sometimes defined subjective probability. In a court of law, question ...

1% chance of guilt has risen to almost 9%. If the prosecution had made the greater claim that the probability of finding the inc ...

33 The birthday problem Imagine you are on the top deck of the Clapham omnibus with nothing in particular to do but count your f ...

probability that yet another person selected at random shares a birthday with the first two is 2/365 so the probability this per ...

Other birthday problems The birthday problem has been generalized in many ways. One approach is to consider three people sharing ...

same birthday? Another question: How many people go into the concert hall before a person turns up with the same birthday as Mr ...

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34 Distributions Ladislaus J. Bortkiewicz was fascinated by mortality tables. Not for him a gloomy topic, they were a field of e ...

The Poisson formula Thankfully, being killed by a horse-kick is a rare event. The most suitable theoretical technique for modell ...

Yesterday I conducted a little experiment. I looked through the foreign currency exchange data in a national newspaper. There we ...

range of texts were analysed, but it will not vary much. It is not surprising that ‘the’ is the most common, and ‘of’ is second. ...