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)