What is the probability that a randomly selected integer in the set { 1, 2, 3 ... 100 } is divisible by 2 and not divisible by 8? Express your answer as a common fraction.
+678 \(\frac{\mbox{Total number of all possible solutions}}{\mbox{Total number of all solutions}}\)
You can choose 100 numbers so
\(\frac{n}{100}\) .
There are 50 numbers that are divisible by 2 in the set { 1, 2, 3, ..., 100 }.
In the set { 1, 2, 3, ..., 100 } there are 12 numbers divisible by 8.
Every multiple of 8 is divisible by 2, so (50 - 12 =) 38 possible solutions. (n = 38)
\(\frac{38}{100} = \frac{19}{50} = 0.38 = 38\%\)
