What is the probability of a number picked from twenty natural numbers is even composite number
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My Thought :
Probability=n(E)/n(S)
Here n(S) is the set of all natural numbers i.e. N, and n(E) is set of all even natural numbers.
Since it is proved that number of elements is the set N is exactly the same as the number of elements in the set of natural numbers
(it’s very easy to put the set of natural numbers, N={0,1,2,3,…}, into one-to-one correspondence with the set E={0,2,4,6,…} of even natural numbers; the map N→E:n↦2n is clearly a bijection.) ;
Thus, Probability =1
Probability=n(E)/n(S)
Here n(S) is the set of all natural numbers i.e. N, and n(E) is set of all even natural numbers.
Since it is proved that number of elements is the set N is exactly the same as the number of elements in the set of natural numbers
(it’s very easy to put the set of natural numbers, N={0,1,2,3,…}, into one-to-one correspondence with the set E={0,2,4,6,…} of even natural numbers; the map N→E:n↦2n is clearly a bijection.) ;
Thus, Probability =1
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