Question

An integer is chosen between 0 and 100. What is the probability that it is
(i) Divisible by 7
(ii) Not divisible by 9

Answer 1

Hint:We know the probability of any event is given by the formula
${\text{Probability}} =
\dfrac{{Number\;of\;favourable\;conditions}}{{Total\;number\;of\;outcomes}}$

In this question for the given two conditions we will first find all the numbers which are between 0 and 100 that are favoring the given conditions and since we are needed to find the numbers between 0 and 100 so the total numbers of outcomes will be 100.

By substituting the values in the formula we will find the probability for both the given conditions.

Complete step by step solution:
(i) The event is to find the number which are divisible by 7 and are between 0 and 100

The total numbers outcomes to choose number between 0 and 100 will be\[ = 99\]

Also the numbers which are between 0 and 100 and are divisible by 7 will be
\[7,14,21,28,35,42,49,56,63,70,77,84,91,98\]

Hence the total numbers of favorable outcomes will be\[ = 14\]

Therefore the probability of choosing numbers between 0 and 100 that is divisible by 7 \[ =
\dfrac{{14}}{{99}}\]

(ii) Here the event is to find the number which are not divisible by 9 and are between 0 and 100
The total numbers outcomes to choose number between 0 and 100 will be\[ = 99\]

To find the answer for numbers not divisible by 9 first we will find the numbers which are divisible by 9,

hence the numbers which are between 0 and 100 and are divisible by 9 will be
\[9,18,27,36,45,54,63,72,81,90,99\]

Hence the total numbers of favorable outcomes will be\[ = 11\]

Therefore the probability of choosing numbers between 0 and 100 that is not divisible by 9
\[
P = 1 - \dfrac{{11}}{{99}} \\
= \dfrac{{88}}{{99}} \\

= \dfrac{8}{9} \\
\]

Note:Binomial distribution formula is given as \[q = 1 - p\], where \[q\]denotes the probability which is not in the favour and\[p\]is the probability which is in the favour. If finding the probability of an event to occur is difficult to find then first we find the probability of an event to not to occur and then by using the Binomial distribution formula we find the probability of an event to occur.