Question

An integer is chosen at random from first two hundred natural numbers. What is the probability that the integer chosen is divisible by 6 or 8?

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

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

$A:Integerchosenisdivisibleby6$

$B:Integerchosenisdivisibleby8$

$n\left(A\right)=33,n\left(B\right)=25,n(A\cap B)=8,n\left(S\right)=200$

$P\left(A\right)=\frac{33}{200},P\left(B\right)=\frac{25}{200}$

$P(A\cup B)=P\left(A\right)+P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{33}{200}+\frac{25}{200}-\frac{8}{200}=\frac{50}{200}=\frac{1}{4}$