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.

Guest Feb 4, 2022

#1**+1 **

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**.

Straight Feb 4, 2022