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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
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In this podcast author Coralie Colmez shares insights into her novel The irrational diary of Clara Valentine.
We talk to early career mathematicians who spent some of their summer holiday solving problems posed by industry — such as how to blend a perfect smoothie!
It makes no difference whether the first envelope is opened, as there is no warrant within the game to assume that any amount is "reasonably" likely to be present. We do not know the universe from which the pairs of envelopes are drawn, so we can make no assumption about it. The "default" assumption about equal likelihood is simply us putting frog DNA where the dinosaur DNA is missing. That is not allowed. We have insufficient information on which to do any math at all.