Can you find a 5?
You are given the set of all whole numbers. You select a number at random from the set . If the probability that the number you get has the digit 5 is P . Find the Value of P - 0.2
Notes
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A number, say 52221 has the digit 5
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The problem is not original
The answer is 0.8.
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1 solution
This problem made me look at numbers in a way I have never seen before.
The answer is 1 . Yes , it is one but lets see how.
Let us consider a n digit positive number.
The total numbers possible are 1 0 n
That is we have n space which can be filled with 10 digits each
Now if we consider all the numbers which do not have the digit 5 are 9 n as the n spaces can be filled with 10-1 digits ( That is we have removed 5)
Therefore the numbers having the digit 5 are 1 0 n - 9^[n}
Hence probability of finding a number with digit 5 is
10^{n} - 9^[n} / 1 0 n
or 1- (0.9)^n
Now for the set of all whole numbers , n tends to infinity. Hence the probability tends to 1.
Isn't this one of the most unusual yet most amazing thing