probability of number ending in 1

perusal

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Jan 7, 2019
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Question: what is the probability of a randomly selected positive integer raised to an arbitrary positive integer ending in the number 1?

The answer is 0.04 I am unsure how this can be arrived at.

My understanding is that any integer ending in 1 will always end in 1 when raised to any positive integer.
No even number will ever end in 1 when raised to any positive integer.
Numbers ending in 9 will end in a 1 when raised to any multiple of 2
Numbers 3 and 7 will end in 1 when raised to any multiple of 4.
Numbers ending in 5 will never end in a 1.
 

pka

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Jan 29, 2005
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Question: what is the probability of a randomly selected positive integer raised to an arbitrary positive integer ending in the number 1?
The answer is 0.04 I am unsure how this can be arrived at.
My understanding is that any integer ending in 1 will always end in 1 when raised to any positive integer.
No even number will ever end in 1 when raised to any positive integer.
Numbers ending in 9 will end in a 1 when raised to any multiple of 2
Numbers 3 and 7 will end in 1 when raised to any multiple of 4.
Numbers ending in 5 will never end in a 1.
What is probability that a randomly selected positive integer ends in \(\displaystyle 3\text{ or } 7~?\) Is it \(\displaystyle \dfrac{2}{10}~?\)
What is probability that a randomly selected positive integral power is a multiple of \(\displaystyle 4~?\)
Repeat that process for \(\displaystyle 1~\&~9\). What do you get?

I see that the provided answer is \(\displaystyle 0.04\) and I get \(\displaystyle 0.23\) see here.
 
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