Probabilities in Carland
In Carland, there is an infinite amount of cars, each with a license plate which has a random number from 0 to 999. Two of those cars are randomly chosen.
Is there a higher probability that both cars will have the same number,
or that one of the numbers is twice as large as the other?
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1 solution
probability of take a number = 1 probability of taking the same number = 1/1000 probability of taking 2 equal numbers = 1 * 1/1000 = 1/1000
given I take a odd number <= 499 it has a double If I take a even number <=499 it has a double anda a half (2 for each) If I take a even number > 499 it has a half for zero whe have only the case 0 0
since there are 250 odd number <= 499, 259 even numbers <= 499 and 250 even number > 500 then there are 250 + 249 * 2 + 250 + 1(for zero) = 999 ways to get a number and then its half or double
the probability of taking 2 numbers one is the double of the other is then 999/(1000*1000) < 1/1000