# A number is chosen from the numbers 1 to 100. Find the probability of its being divisible by 4 or 6.

let A denote the event that the number is divisible by 4 and B denote the event that the number is divisible by 4.

To find : Probability that the number is both divisible by 4 or 6 = P(A or B)

The formula used : Probability = P(A or B) = P(A) + P(B) - P(A and B)

Numbers from 1 to 100 divisible by 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100.

There are 25 numbers from 1 to 100 divisible by 4

Favourable number of outcomes = 25

Total number of outcomes = 100 as there are 100 numbers from 1 to 100

P(A) = Numbers from 1 to 100 divisible by 6 are

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96

There are 16 numbers from 1 to 100 divisible by 6

Favourable number of outcomes = 16

Total number of outcomes = 100 as there are 100 numbers from 1 to 100

P(B) = Numbers from 1 to 100 divisible by both 4 and 6 are

12,24,36,48,60,72,84,96

There are 8 numbers from 1 to 100 divisible by both 4 and 6

Favourable number of outcomes = 8

P(A and B) = P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(A or B) = P(A or B) The probability that the number is both divisible by 4 or 6 = P(A or B) Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 