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If the car is behind door 1, the host can open either door 2 or door 3, so the probability that the car is behind door 1 and the host opens door 3 is 1 / 3 × 1 / 2 = 1 / 6 . If the car is behind door 2 – with the player having picked door 1 – the host must open door 3, such the probability that the car is behind door ...
Imagine what might be in the first envelope. A sensible strategy would certainly be to swap when the first envelope contains 1, as the other must then contain 2. Suppose on the other hand the first envelope contains 2. In that case, there are two possibilities: the envelope pair in front of us is either {1, 2} or {2, 4}. All other pairs are ...
A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be 1 / 2 , but the probability is actually 2 / 3 . [1] Bertrand showed that if 1 / 2 were correct, it would result in a contradiction, so 1 / 2 ...
In game theory, "guess 2 / 3 of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to 2 / 3 of the average of numbers chosen by all players. [1]
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Pick a randomly in the range [2, n − 2] If (), then return composite If composite is never returned: return probably prime. The a values 1 and n-1 are not used as the equality holds for all n and all odd n respectively, hence testing them adds no value.
Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. [note 1] For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often ...
An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion ), the search path of a foraging animal, or the price of a fluctuating ...