Once I read a magazine article about probability where the author stated there was an unlikely event. The probability was given as
(1 - 10-21)1025
This probability is pretty small but hard to get a handle on. It is, however, quite close to 10-n, where n is an integer.
Find this integer.
This obviously calls for logarithms. We're going to need to find the common logarithm of 1-10^-21 and multiply it by a 25-digit number (well, actually 26 digits, but on the borderline--don't count on it for 26-digit precision).
The logarithm itself will be close to zero, having about 21 zeros after the decimal to even get to the first significant digit. We'll need about four or five significant digits to get an integral approximation, but we should go for more to see how close n really is to an integer.
Wolfram Alpha gives us many more significant digits than we need:
Asking Wolfram Alpha for log(1-10^-21)*10^25, and asking for use of common logs, gives
-4342.94481903251827651346066157556708208222715027952169...
so the integer n in the puzzle is 4343.
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Posted by Charlie
on 2019-02-21 11:37:43 |
solution
