Question

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

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{4}$

One integer can be chosen out of $200$ integer in ${}^{200}{C}_1$ ways.
Let A be event than an integer selected is divisible by 6 and B that it is divisible by 8.

Then, $P\left(A\right)=\frac{33}{200},P\left(B\right)=\frac{25}{200}$ and $P(A\cap B)=\frac{8}{192}$

$\therefore$ Required probability $=P(A\cup B)$

$=P\left(A\right)+P\left(B\right)-P(A\cap B)$$=\frac{33}{200}+\frac{25}{200}-\frac{8}{192}=\frac{1}{4}$