What is the probability that a randomly selected integer in the set { 1, 2, 3 ... 100 } is divisible by 2 and not divisible by 6? Express your answer as a common fraction.
+678 ugh...
When I wanted to click "Show Preview", they deleted my answer...
So... here we go again:
\(\frac{\mbox{Total number of all possible solutions}}{\mbox{Total number of all solutions}}\)
In the set, we can choose 100 numbers \(\Rightarrow\)\(\frac{n}{100}\), where n is a positive integer.
From those 100 numbers, ( 100 / 2 = ) 50 numbers are divisible by 2.
From those 50 numbers,
50 / 6 = 8 mod 2 \(\Rightarrow\) 8 numbers
are divisible by 6.
Subtract both numbers \(\Rightarrow\) 50 - 8 = 42 numbers, so
42 / 100 = 21 / 50 .
Thus, our answer is 21 / 50.
