An integer is chosen between 0 and 100.

Question:

An integer is chosen between 0 and 100. What is the probability that it is

(i) divisible by 7?                         

(ii) not divisible by 7?

Solution:

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

$\therefore \quad n\left(E_{2}\right)=n(S)-n\left(E_{1}\right)$

$=99-14=85$

$\therefore$ $P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{85}{99}$

Leave a comment

Close
faculty

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.

Download Now