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?
By all means calculate the expected amount in envelope B as 5x/4 if you like. But since you're switching, you're giving up the amount in envelope A, which is x. So the expected gain on the switch must be 5x/4 - x = x/4
But what if it's A that contains 2x or x/2 and you switch it for B containing x? Then the expected gain is the result of reversing the subtraction in the above EV equation, namely x - 5x/4 = -x/4. Symmetry.
If you can't know which envelope is which, then you can't know either the advantage or disadvantage, the gain or loss, to switching. The expected gains, positive and negative, cancel. Symmetry.
If you know that A contains x, then sure, you switch. If you know A contains x/2 or 2x, then sure, you don't switch. Symmetry.