An integer is chosen between 0 and 100. What is the probability that it is
(i) divisible by 7?
(ii) not divisible by 7?
The number of integers between 0 and 100 is
n(S)= 99
(i) Let $E_{1}=$ Event of choosing an integer which is divisible by 7
$=$ Event of choosing an integer which is multiple of 7
$=\{7,14,21,28,35,42,49,56,63,70,77,84,91,98\}$
$\therefore \quad n\left(E_{1}\right)=14$
$\therefore \quad P\left(E_{1}\right)=\frac{n\left(E_{1}\right)}{n(S)}=\frac{14}{99}$
(ii) Let $E_{2}=$ Event of choosing an integer which is not divisible by 7
$\therefore \quad n\left(E_{2}\right)=n(S)-n\left(E_{1}\right)$
$=99-14=85$
$\therefore$ $P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{85}{99}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.