Y is a real number which is chosen at random from the interval (0,1).
Determine the probability that floor(log_{10}(4Y)) = floor(log_{10}Y)
The probablity is 1/6.
First consider only the numbers for which the first nonzero digit is in the 10ths column. For the numbers 0.1 <= Y < 0.25, then .4 <= 4Y < 1 and the condition is met for a probability of 0.15
For numbers for which the first nonzero digit is in the 100ths column, the condition is met for 0.015 since 0.01 <= Y < 0.025, then .04 <= 4Y < .1
So the answer is 0.15 times the infinite series 1+a+a^2+a^3+ ... where a=1/10.
And 0.15 * 10/9 = 1/6

Posted by Larry
on 20140803 12:18:32 