Add new comment
-
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.
Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.
Find out why the formula we use to work out conditional probabilities is true!
We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.
News stories have claimed they may have — but is this true?
If you ask a child to choose a random number from 1 to a million, and he says something like 5, then it's likely he really didn't really randomize his choice.
If you are asked to choose a random positive number (with no other restrictions) then:
P(The number is less than 10) = 0.
P(The number is less than 100) = 0.
P(The number is less than any arbitrarily chosen number, N) = 0.
It is thus impossible to choose a random number with no constraints.
More technically:
P(A | B) where:
A: The number you have chosen is truly random
B: The number you have chosen is less than any arbitrary number, N
is given by:
P(A|B) = P(A Intersect B) / P(B)
The numerator is 0. The denominator is not.
Thus the problem is poorly formed.
If you restrict the maximum amount of money so some value, then the problem is trivial and whether or not you should switch (assuming you examine the contents of the chosen envelope before deciding whether or not to switch) is an easy calculation.
(I think)