question_answer

An integer is chosen at random from the first two hundred digits. The probability that the integer chosen is divisible by 6 or 8 is:

A) (a) \[\frac{3}{4}\]                      

B) (b) \[\frac{1}{2}\]              

C) (c) \[\frac{1}{4}\]                                  

D) (d) \[\frac{2}{3}\]

Correct Answer: C

Solution :

[c] Let A = integer chosen is divisible by 6 \[=\left\{ 6,12,18,......198 \right\}\] B = integer chosen is divisible by 8 \[=\left\{ 8,16,24,.........\text{ }200 \right\}\] \[\therefore p\left( A \right)=\frac{33}{100}.Simlarly,P\left( B \right)=\frac{25}{200}\And P\left( A\cap B \right)=\frac{8}{200}\]               \[\therefore \] Required probability \[=P(A\cup B)=P(A).P(B)-P(A\cap B)\] \[=\frac{33}{200}+\frac{25}{200}-\frac{8}{200}=\frac{50}{200}=\frac{1}{4}\] Hence, option [c]is correct.