Question

An integer is chosen at random from the first $200$ positive integers. The probability that the integer chosen is divisible by $6$ or $8$ is

• A. $\frac{1}{4}$
• B. $\frac{2}{3}$
• C. $\frac{1}{5}$
• D. $0$

Answer 1

Answer: (A)

$\frac{1}{4}$

The number of numbers which are divisible by $6$ which are less than $200$ is $33$.

The number of numbers which are divisible by $8$ which are less than $200$ is $25$.

The number of numbers which are divisible by both $6$ and $8$ which are less than $200$ is $8$.

Therefore the number of numbers which are divisible by $6$ or $8$ is $33+25-8=50$.

The probability is $\frac{50}{200}=\frac{1}{4}$.

The correct option is $A$.